TSTP Solution File: SEU104+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n021.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 10:57:36 EDT 2023

% Result   : Theorem 7.13s 2.76s
% Output   : CNFRefutation 7.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   93 (  23 unt;  34 typ;   0 def)
%            Number of atoms       :  125 (   7 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  129 (  63   ~;  53   |;   4   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  28   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   6 con; 0-2 aty)
%            Number of variables   :   66 (;  66   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > symmetric_difference > set_union2 > set_difference > #nlpp > powerset > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_1 > #skF_5 > #skF_10 > #skF_13 > #skF_2 > #skF_3 > #skF_8 > #skF_11 > #skF_12 > #skF_6

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_13',type,
    '#skF_13': $i ).

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

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

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

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

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

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

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

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

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

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

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

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

tff(f_204,negated_conjecture,
    ~ ! [A] :
        ( ~ empty(A)
       => ( ! [B] :
              ( element(B,A)
             => ! [C] :
                  ( element(C,A)
                 => ( in(symmetric_difference(B,C),A)
                    & in(set_difference(B,C),A) ) ) )
         => preboolean(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finsub_1) ).

tff(f_177,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_188,axiom,
    ! [A] :
      ( preboolean(A)
    <=> ! [B,C] :
          ( ( in(B,A)
            & in(C,A) )
         => ( in(set_union2(B,C),A)
            & in(set_difference(B,C),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).

tff(f_222,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

tff(f_230,axiom,
    ! [A,B,C] :
      ( ( in(A,B)
        & element(B,powerset(C)) )
     => element(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

tff(f_258,axiom,
    ! [A,B] : ( set_union2(A,B) = symmetric_difference(A,set_difference(B,A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).

tff(f_56,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_210,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

tff(f_97,axiom,
    ! [A,B] : ( set_union2(A,A) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

tff(c_108,plain,
    ~ preboolean('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_96,plain,
    ! [A_40] : subset(A_40,A_40),
    inference(cnfTransformation,[status(thm)],[f_177]) ).

tff(c_106,plain,
    ! [A_42] :
      ( in('#skF_11'(A_42),A_42)
      | preboolean(A_42) ),
    inference(cnfTransformation,[status(thm)],[f_188]) ).

tff(c_126,plain,
    ! [A_61,B_62] :
      ( element(A_61,powerset(B_62))
      | ~ subset(A_61,B_62) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_1026,plain,
    ! [A_188,C_189,B_190] :
      ( element(A_188,C_189)
      | ~ element(B_190,powerset(C_189))
      | ~ in(A_188,B_190) ),
    inference(cnfTransformation,[status(thm)],[f_230]) ).

tff(c_1480,plain,
    ! [A_221,B_222,A_223] :
      ( element(A_221,B_222)
      | ~ in(A_221,A_223)
      | ~ subset(A_223,B_222) ),
    inference(resolution,[status(thm)],[c_126,c_1026]) ).

tff(c_1498,plain,
    ! [A_42,B_222] :
      ( element('#skF_11'(A_42),B_222)
      | ~ subset(A_42,B_222)
      | preboolean(A_42) ),
    inference(resolution,[status(thm)],[c_106,c_1480]) ).

tff(c_104,plain,
    ! [A_42] :
      ( in('#skF_12'(A_42),A_42)
      | preboolean(A_42) ),
    inference(cnfTransformation,[status(thm)],[f_188]) ).

tff(c_1499,plain,
    ! [A_42,B_222] :
      ( element('#skF_12'(A_42),B_222)
      | ~ subset(A_42,B_222)
      | preboolean(A_42) ),
    inference(resolution,[status(thm)],[c_104,c_1480]) ).

tff(c_870,plain,
    ! [A_174,B_175] : ( symmetric_difference(A_174,set_difference(B_175,A_174)) = set_union2(A_174,B_175) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_114,plain,
    ! [B_52,C_54] :
      ( in(symmetric_difference(B_52,C_54),'#skF_13')
      | ~ element(C_54,'#skF_13')
      | ~ element(B_52,'#skF_13') ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_886,plain,
    ! [A_174,B_175] :
      ( in(set_union2(A_174,B_175),'#skF_13')
      | ~ element(set_difference(B_175,A_174),'#skF_13')
      | ~ element(A_174,'#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_870,c_114]) ).

tff(c_14,plain,
    ! [B_10,A_9] : ( set_union2(B_10,A_9) = set_union2(A_9,B_10) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_102,plain,
    ! [A_42] :
      ( ~ in(set_difference('#skF_11'(A_42),'#skF_12'(A_42)),A_42)
      | ~ in(set_union2('#skF_11'(A_42),'#skF_12'(A_42)),A_42)
      | preboolean(A_42) ),
    inference(cnfTransformation,[status(thm)],[f_188]) ).

tff(c_1699,plain,
    ! [A_241] :
      ( ~ in(set_difference('#skF_11'(A_241),'#skF_12'(A_241)),A_241)
      | ~ in(set_union2('#skF_12'(A_241),'#skF_11'(A_241)),A_241)
      | preboolean(A_241) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_102]) ).

tff(c_1703,plain,
    ( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
    | preboolean('#skF_13')
    | ~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
    | ~ element('#skF_12'('#skF_13'),'#skF_13') ),
    inference(resolution,[status(thm)],[c_886,c_1699]) ).

tff(c_1714,plain,
    ( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
    | ~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
    | ~ element('#skF_12'('#skF_13'),'#skF_13') ),
    inference(negUnitSimplification,[status(thm)],[c_108,c_1703]) ).

tff(c_2563,plain,
    ~ element('#skF_12'('#skF_13'),'#skF_13'),
    inference(splitLeft,[status(thm)],[c_1714]) ).

tff(c_2566,plain,
    ( ~ subset('#skF_13','#skF_13')
    | preboolean('#skF_13') ),
    inference(resolution,[status(thm)],[c_1499,c_2563]) ).

tff(c_2572,plain,
    preboolean('#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_2566]) ).

tff(c_2574,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_108,c_2572]) ).

tff(c_2576,plain,
    element('#skF_12'('#skF_13'),'#skF_13'),
    inference(splitRight,[status(thm)],[c_1714]) ).

tff(c_112,plain,
    ! [B_52,C_54] :
      ( in(set_difference(B_52,C_54),'#skF_13')
      | ~ element(C_54,'#skF_13')
      | ~ element(B_52,'#skF_13') ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_1501,plain,
    ! [B_52,C_54,B_222] :
      ( element(set_difference(B_52,C_54),B_222)
      | ~ subset('#skF_13',B_222)
      | ~ element(C_54,'#skF_13')
      | ~ element(B_52,'#skF_13') ),
    inference(resolution,[status(thm)],[c_112,c_1480]) ).

tff(c_142,plain,
    ! [A_76,B_77] : ( symmetric_difference(A_76,set_difference(B_77,A_76)) = set_union2(A_76,B_77) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_596,plain,
    ! [A_131,B_132] :
      ( element(A_131,B_132)
      | ~ in(A_131,B_132) ),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_983,plain,
    ! [B_182,C_183] :
      ( element(symmetric_difference(B_182,C_183),'#skF_13')
      | ~ element(C_183,'#skF_13')
      | ~ element(B_182,'#skF_13') ),
    inference(resolution,[status(thm)],[c_114,c_596]) ).

tff(c_4280,plain,
    ! [A_374,B_375] :
      ( element(set_union2(A_374,B_375),'#skF_13')
      | ~ element(set_difference(B_375,A_374),'#skF_13')
      | ~ element(A_374,'#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_142,c_983]) ).

tff(c_36,plain,
    ! [A_28] : ( set_union2(A_28,A_28) = A_28 ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_1399,plain,
    ! [A_215,B_216] :
      ( in(set_union2(A_215,B_216),'#skF_13')
      | ~ element(set_difference(B_216,A_215),'#skF_13')
      | ~ element(A_215,'#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_870,c_114]) ).

tff(c_2656,plain,
    ! [A_310] :
      ( in(A_310,'#skF_13')
      | ~ element(set_difference(A_310,A_310),'#skF_13')
      | ~ element(A_310,'#skF_13') ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_1399]) ).

tff(c_2660,plain,
    ! [C_54] :
      ( in(C_54,'#skF_13')
      | ~ subset('#skF_13','#skF_13')
      | ~ element(C_54,'#skF_13') ),
    inference(resolution,[status(thm)],[c_1501,c_2656]) ).

tff(c_2677,plain,
    ! [C_311] :
      ( in(C_311,'#skF_13')
      | ~ element(C_311,'#skF_13') ),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_2660]) ).

tff(c_143,plain,
    ! [A_42] :
      ( ~ in(set_difference('#skF_11'(A_42),'#skF_12'(A_42)),A_42)
      | ~ in(set_union2('#skF_12'(A_42),'#skF_11'(A_42)),A_42)
      | preboolean(A_42) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_102]) ).

tff(c_2681,plain,
    ( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
    | preboolean('#skF_13')
    | ~ element(set_union2('#skF_12'('#skF_13'),'#skF_11'('#skF_13')),'#skF_13') ),
    inference(resolution,[status(thm)],[c_2677,c_143]) ).

tff(c_2699,plain,
    ( ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
    | ~ element(set_union2('#skF_12'('#skF_13'),'#skF_11'('#skF_13')),'#skF_13') ),
    inference(negUnitSimplification,[status(thm)],[c_108,c_2681]) ).

tff(c_2773,plain,
    ~ element(set_union2('#skF_12'('#skF_13'),'#skF_11'('#skF_13')),'#skF_13'),
    inference(splitLeft,[status(thm)],[c_2699]) ).

tff(c_4286,plain,
    ( ~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13')
    | ~ element('#skF_12'('#skF_13'),'#skF_13') ),
    inference(resolution,[status(thm)],[c_4280,c_2773]) ).

tff(c_4316,plain,
    ~ element(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_2576,c_4286]) ).

tff(c_4327,plain,
    ( ~ subset('#skF_13','#skF_13')
    | ~ element('#skF_12'('#skF_13'),'#skF_13')
    | ~ element('#skF_11'('#skF_13'),'#skF_13') ),
    inference(resolution,[status(thm)],[c_1501,c_4316]) ).

tff(c_4334,plain,
    ~ element('#skF_11'('#skF_13'),'#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_2576,c_96,c_4327]) ).

tff(c_4340,plain,
    ( ~ subset('#skF_13','#skF_13')
    | preboolean('#skF_13') ),
    inference(resolution,[status(thm)],[c_1498,c_4334]) ).

tff(c_4346,plain,
    preboolean('#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_4340]) ).

tff(c_4348,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_108,c_4346]) ).

tff(c_4349,plain,
    ~ in(set_difference('#skF_11'('#skF_13'),'#skF_12'('#skF_13')),'#skF_13'),
    inference(splitRight,[status(thm)],[c_2699]) ).

tff(c_4362,plain,
    ( ~ element('#skF_12'('#skF_13'),'#skF_13')
    | ~ element('#skF_11'('#skF_13'),'#skF_13') ),
    inference(resolution,[status(thm)],[c_112,c_4349]) ).

tff(c_4370,plain,
    ~ element('#skF_11'('#skF_13'),'#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_2576,c_4362]) ).

tff(c_4373,plain,
    ( ~ subset('#skF_13','#skF_13')
    | preboolean('#skF_13') ),
    inference(resolution,[status(thm)],[c_1498,c_4370]) ).

tff(c_4379,plain,
    preboolean('#skF_13'),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_4373]) ).

tff(c_4381,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_108,c_4379]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU104+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.13/0.34  % Computer : n021.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 : Thu Aug  3 11:41:36 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 7.13/2.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.13/2.77  
% 7.13/2.77  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.13/2.80  
% 7.13/2.80  Inference rules
% 7.13/2.80  ----------------------
% 7.13/2.80  #Ref     : 0
% 7.13/2.80  #Sup     : 973
% 7.13/2.80  #Fact    : 0
% 7.13/2.80  #Define  : 0
% 7.13/2.80  #Split   : 19
% 7.13/2.80  #Chain   : 0
% 7.13/2.80  #Close   : 0
% 7.13/2.80  
% 7.13/2.80  Ordering : KBO
% 7.13/2.80  
% 7.13/2.80  Simplification rules
% 7.13/2.80  ----------------------
% 7.13/2.80  #Subsume      : 273
% 7.13/2.80  #Demod        : 388
% 7.13/2.80  #Tautology    : 250
% 7.13/2.80  #SimpNegUnit  : 64
% 7.13/2.80  #BackRed      : 13
% 7.13/2.80  
% 7.13/2.80  #Partial instantiations: 0
% 7.13/2.80  #Strategies tried      : 1
% 7.13/2.80  
% 7.13/2.80  Timing (in seconds)
% 7.13/2.80  ----------------------
% 7.41/2.80  Preprocessing        : 0.56
% 7.41/2.80  Parsing              : 0.30
% 7.41/2.81  CNF conversion       : 0.05
% 7.41/2.81  Main loop            : 1.18
% 7.41/2.81  Inferencing          : 0.42
% 7.41/2.81  Reduction            : 0.37
% 7.41/2.81  Demodulation         : 0.26
% 7.41/2.81  BG Simplification    : 0.04
% 7.41/2.81  Subsumption          : 0.26
% 7.41/2.81  Abstraction          : 0.03
% 7.41/2.81  MUC search           : 0.00
% 7.41/2.81  Cooper               : 0.00
% 7.41/2.81  Total                : 1.80
% 7.41/2.81  Index Insertion      : 0.00
% 7.41/2.81  Index Deletion       : 0.00
% 7.41/2.81  Index Matching       : 0.00
% 7.41/2.81  BG Taut test         : 0.00
%------------------------------------------------------------------------------