TSTP Solution File: SEU320+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n020.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 10:58:24 EDT 2023

% Result   : Theorem 3.50s 1.90s
% Output   : CNFRefutation 3.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   43 (  14 unt;  14 typ;   0 def)
%            Number of atoms       :   56 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   53 (  26   ~;  19   |;   0   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  10   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (;  18   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > open_subset > element > closed_subset > top_str > one_sorted_str > subset_complement > #nlpp > the_carrier > powerset > #skF_5 > #skF_2 > #skF_1 > #skF_4 > #skF_3

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_67,negated_conjecture,
    ~ ! [A] :
        ( top_str(A)
       => ! [B] :
            ( element(B,powerset(the_carrier(A)))
           => ( open_subset(B,A)
            <=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).

tff(f_31,axiom,
    ! [A,B] :
      ( element(B,powerset(A))
     => element(subset_complement(A,B),powerset(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).

tff(f_46,axiom,
    ! [A,B] :
      ( element(B,powerset(A))
     => ( subset_complement(A,subset_complement(A,B)) = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

tff(f_57,axiom,
    ! [A] :
      ( top_str(A)
     => ! [B] :
          ( element(B,powerset(the_carrier(A)))
         => ( closed_subset(B,A)
          <=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).

tff(c_28,plain,
    element('#skF_5',powerset(the_carrier('#skF_4'))),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_4,plain,
    ! [A_1,B_2] :
      ( element(subset_complement(A_1,B_2),powerset(A_1))
      | ~ element(B_2,powerset(A_1)) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_32,plain,
    ( ~ closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
    | ~ open_subset('#skF_5','#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_54,plain,
    ~ open_subset('#skF_5','#skF_4'),
    inference(splitLeft,[status(thm)],[c_32]) ).

tff(c_30,plain,
    top_str('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_38,plain,
    ( open_subset('#skF_5','#skF_4')
    | closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_71,plain,
    closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_54,c_38]) ).

tff(c_72,plain,
    ! [A_24,B_25] :
      ( ( subset_complement(A_24,subset_complement(A_24,B_25)) = B_25 )
      | ~ element(B_25,powerset(A_24)) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_81,plain,
    subset_complement(the_carrier('#skF_4'),subset_complement(the_carrier('#skF_4'),'#skF_5')) = '#skF_5',
    inference(resolution,[status(thm)],[c_28,c_72]) ).

tff(c_249,plain,
    ! [A_35,B_36] :
      ( open_subset(subset_complement(the_carrier(A_35),B_36),A_35)
      | ~ closed_subset(B_36,A_35)
      | ~ element(B_36,powerset(the_carrier(A_35)))
      | ~ top_str(A_35) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_264,plain,
    ( open_subset('#skF_5','#skF_4')
    | ~ closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
    | ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4')))
    | ~ top_str('#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_81,c_249]) ).

tff(c_266,plain,
    ( open_subset('#skF_5','#skF_4')
    | ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_71,c_264]) ).

tff(c_267,plain,
    ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))),
    inference(negUnitSimplification,[status(thm)],[c_54,c_266]) ).

tff(c_270,plain,
    ~ element('#skF_5',powerset(the_carrier('#skF_4'))),
    inference(resolution,[status(thm)],[c_4,c_267]) ).

tff(c_277,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_270]) ).

tff(c_278,plain,
    ~ closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4'),
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_279,plain,
    open_subset('#skF_5','#skF_4'),
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_298,plain,
    ! [A_42,B_43] :
      ( ( subset_complement(A_42,subset_complement(A_42,B_43)) = B_43 )
      | ~ element(B_43,powerset(A_42)) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_307,plain,
    subset_complement(the_carrier('#skF_4'),subset_complement(the_carrier('#skF_4'),'#skF_5')) = '#skF_5',
    inference(resolution,[status(thm)],[c_28,c_298]) ).

tff(c_475,plain,
    ! [B_53,A_54] :
      ( closed_subset(B_53,A_54)
      | ~ open_subset(subset_complement(the_carrier(A_54),B_53),A_54)
      | ~ element(B_53,powerset(the_carrier(A_54)))
      | ~ top_str(A_54) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_490,plain,
    ( closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
    | ~ open_subset('#skF_5','#skF_4')
    | ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4')))
    | ~ top_str('#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_307,c_475]) ).

tff(c_492,plain,
    ( closed_subset(subset_complement(the_carrier('#skF_4'),'#skF_5'),'#skF_4')
    | ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_279,c_490]) ).

tff(c_493,plain,
    ~ element(subset_complement(the_carrier('#skF_4'),'#skF_5'),powerset(the_carrier('#skF_4'))),
    inference(negUnitSimplification,[status(thm)],[c_278,c_492]) ).

tff(c_496,plain,
    ~ element('#skF_5',powerset(the_carrier('#skF_4'))),
    inference(resolution,[status(thm)],[c_4,c_493]) ).

tff(c_503,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_496]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13  % 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
% 0.14/0.34  % Computer : n020.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 12:09:22 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 3.50/1.90  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.50/1.91  
% 3.50/1.91  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.75/1.94  
% 3.75/1.94  Inference rules
% 3.75/1.94  ----------------------
% 3.75/1.94  #Ref     : 0
% 3.75/1.94  #Sup     : 104
% 3.75/1.94  #Fact    : 0
% 3.75/1.94  #Define  : 0
% 3.75/1.94  #Split   : 1
% 3.75/1.94  #Chain   : 0
% 3.75/1.94  #Close   : 0
% 3.75/1.94  
% 3.75/1.94  Ordering : KBO
% 3.75/1.94  
% 3.75/1.94  Simplification rules
% 3.75/1.94  ----------------------
% 3.75/1.94  #Subsume      : 6
% 3.75/1.94  #Demod        : 35
% 3.75/1.94  #Tautology    : 77
% 3.75/1.94  #SimpNegUnit  : 4
% 3.75/1.94  #BackRed      : 0
% 3.75/1.94  
% 3.75/1.94  #Partial instantiations: 0
% 3.75/1.94  #Strategies tried      : 1
% 3.75/1.94  
% 3.75/1.94  Timing (in seconds)
% 3.75/1.94  ----------------------
% 3.75/1.94  Preprocessing        : 0.47
% 3.75/1.94  Parsing              : 0.26
% 3.75/1.94  CNF conversion       : 0.03
% 3.75/1.94  Main loop            : 0.40
% 3.75/1.94  Inferencing          : 0.17
% 3.75/1.94  Reduction            : 0.11
% 3.75/1.94  Demodulation         : 0.08
% 3.75/1.94  BG Simplification    : 0.02
% 3.75/1.94  Subsumption          : 0.08
% 3.75/1.94  Abstraction          : 0.02
% 3.75/1.94  MUC search           : 0.00
% 3.75/1.94  Cooper               : 0.00
% 3.75/1.94  Total                : 0.92
% 3.75/1.94  Index Insertion      : 0.00
% 3.75/1.94  Index Deletion       : 0.00
% 3.75/1.94  Index Matching       : 0.00
% 3.75/1.94  BG Taut test         : 0.00
%------------------------------------------------------------------------------