TSTP Solution File: SEU131+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU131+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/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 : n028.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 10:57:41 EDT 2023

% Result   : Theorem 13.26s 4.31s
% Output   : CNFRefutation 13.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   67 (  19 unt;  16 typ;   0 def)
%            Number of atoms       :  101 (  30 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   86 (  36   ~;  42   |;   2   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (   9   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-3 aty)
%            Number of variables   :   65 (;  64   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > empty > set_difference > #nlpp > empty_set > #skF_11 > #skF_7 > #skF_5 > #skF_6 > #skF_10 > #skF_2 > #skF_9 > #skF_8 > #skF_4 > #skF_3 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_55,negated_conjecture,
    ~ ! [A,B] :
        ( ( set_difference(A,B) = empty_set )
      <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).

tff(f_38,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_57,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_77,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_48,axiom,
    ! [A,B,C] :
      ( ( C = set_difference(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & ~ in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

tff(f_82,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

tff(c_36,plain,
    ( subset('#skF_4','#skF_5')
    | ~ subset('#skF_6','#skF_7') ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_118,plain,
    ~ subset('#skF_6','#skF_7'),
    inference(splitLeft,[status(thm)],[c_36]) ).

tff(c_8,plain,
    ! [A_3,B_4] :
      ( in('#skF_1'(A_3,B_4),A_3)
      | subset(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_42,plain,
    empty('#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_66,plain,
    ! [A_27] :
      ( ( empty_set = A_27 )
      | ~ empty(A_27) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_73,plain,
    empty_set = '#skF_8',
    inference(resolution,[status(thm)],[c_42,c_66]) ).

tff(c_40,plain,
    ( subset('#skF_4','#skF_5')
    | ( set_difference('#skF_6','#skF_7') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_132,plain,
    ( subset('#skF_4','#skF_5')
    | ( set_difference('#skF_6','#skF_7') = '#skF_8' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_40]) ).

tff(c_133,plain,
    set_difference('#skF_6','#skF_7') = '#skF_8',
    inference(splitLeft,[status(thm)],[c_132]) ).

tff(c_244,plain,
    ! [D_66,A_67,B_68] :
      ( in(D_66,set_difference(A_67,B_68))
      | in(D_66,B_68)
      | ~ in(D_66,A_67) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_62,plain,
    ! [B_23,A_22] :
      ( ~ empty(B_23)
      | ~ in(A_22,B_23) ),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_350,plain,
    ! [A_75,B_76,D_77] :
      ( ~ empty(set_difference(A_75,B_76))
      | in(D_77,B_76)
      | ~ in(D_77,A_75) ),
    inference(resolution,[status(thm)],[c_244,c_62]) ).

tff(c_352,plain,
    ! [D_77] :
      ( ~ empty('#skF_8')
      | in(D_77,'#skF_7')
      | ~ in(D_77,'#skF_6') ),
    inference(superposition,[status(thm),theory(equality)],[c_133,c_350]) ).

tff(c_367,plain,
    ! [D_80] :
      ( in(D_80,'#skF_7')
      | ~ in(D_80,'#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_42,c_352]) ).

tff(c_6,plain,
    ! [A_3,B_4] :
      ( ~ in('#skF_1'(A_3,B_4),B_4)
      | subset(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_405,plain,
    ! [A_82] :
      ( subset(A_82,'#skF_7')
      | ~ in('#skF_1'(A_82,'#skF_7'),'#skF_6') ),
    inference(resolution,[status(thm)],[c_367,c_6]) ).

tff(c_409,plain,
    subset('#skF_6','#skF_7'),
    inference(resolution,[status(thm)],[c_8,c_405]) ).

tff(c_413,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_118,c_118,c_409]) ).

tff(c_415,plain,
    set_difference('#skF_6','#skF_7') != '#skF_8',
    inference(splitRight,[status(thm)],[c_132]) ).

tff(c_38,plain,
    ( ( set_difference('#skF_4','#skF_5') != empty_set )
    | ( set_difference('#skF_6','#skF_7') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_416,plain,
    ( ( set_difference('#skF_4','#skF_5') != '#skF_8' )
    | ( set_difference('#skF_6','#skF_7') = '#skF_8' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_73,c_38]) ).

tff(c_417,plain,
    set_difference('#skF_4','#skF_5') != '#skF_8',
    inference(splitLeft,[status(thm)],[c_416]) ).

tff(c_414,plain,
    subset('#skF_4','#skF_5'),
    inference(splitRight,[status(thm)],[c_132]) ).

tff(c_862,plain,
    ! [A_153,B_154,C_155] :
      ( in('#skF_2'(A_153,B_154,C_155),A_153)
      | in('#skF_3'(A_153,B_154,C_155),C_155)
      | ( set_difference(A_153,B_154) = C_155 ) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_4,plain,
    ! [C_7,B_4,A_3] :
      ( in(C_7,B_4)
      | ~ in(C_7,A_3)
      | ~ subset(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_8063,plain,
    ! [A_482,B_483,C_484,B_485] :
      ( in('#skF_2'(A_482,B_483,C_484),B_485)
      | ~ subset(A_482,B_485)
      | in('#skF_3'(A_482,B_483,C_484),C_484)
      | ( set_difference(A_482,B_483) = C_484 ) ),
    inference(resolution,[status(thm)],[c_862,c_4]) ).

tff(c_24,plain,
    ! [A_8,B_9,C_10] :
      ( ~ in('#skF_2'(A_8,B_9,C_10),B_9)
      | in('#skF_3'(A_8,B_9,C_10),C_10)
      | ( set_difference(A_8,B_9) = C_10 ) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_9627,plain,
    ! [A_545,B_546,C_547] :
      ( ~ subset(A_545,B_546)
      | in('#skF_3'(A_545,B_546,C_547),C_547)
      | ( set_difference(A_545,B_546) = C_547 ) ),
    inference(resolution,[status(thm)],[c_8063,c_24]) ).

tff(c_9708,plain,
    ! [C_548,A_549,B_550] :
      ( ~ empty(C_548)
      | ~ subset(A_549,B_550)
      | ( set_difference(A_549,B_550) = C_548 ) ),
    inference(resolution,[status(thm)],[c_9627,c_62]) ).

tff(c_9712,plain,
    ! [A_551,B_552] :
      ( ~ subset(A_551,B_552)
      | ( set_difference(A_551,B_552) = '#skF_8' ) ),
    inference(resolution,[status(thm)],[c_42,c_9708]) ).

tff(c_9739,plain,
    set_difference('#skF_4','#skF_5') = '#skF_8',
    inference(resolution,[status(thm)],[c_414,c_9712]) ).

tff(c_9755,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_417,c_9739]) ).

tff(c_9756,plain,
    set_difference('#skF_6','#skF_7') = '#skF_8',
    inference(splitRight,[status(thm)],[c_416]) ).

tff(c_9758,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_415,c_9756]) ).

tff(c_9760,plain,
    subset('#skF_6','#skF_7'),
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_34,plain,
    ( ( set_difference('#skF_4','#skF_5') != empty_set )
    | ~ subset('#skF_6','#skF_7') ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_9775,plain,
    set_difference('#skF_4','#skF_5') != '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_9760,c_73,c_34]) ).

tff(c_9759,plain,
    subset('#skF_4','#skF_5'),
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_10147,plain,
    ! [A_617,B_618,C_619] :
      ( in('#skF_2'(A_617,B_618,C_619),A_617)
      | in('#skF_3'(A_617,B_618,C_619),C_619)
      | ( set_difference(A_617,B_618) = C_619 ) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_18821,plain,
    ! [A_993,B_994,C_995,B_996] :
      ( in('#skF_2'(A_993,B_994,C_995),B_996)
      | ~ subset(A_993,B_996)
      | in('#skF_3'(A_993,B_994,C_995),C_995)
      | ( set_difference(A_993,B_994) = C_995 ) ),
    inference(resolution,[status(thm)],[c_10147,c_4]) ).

tff(c_23349,plain,
    ! [A_1102,B_1103,C_1104] :
      ( ~ subset(A_1102,B_1103)
      | in('#skF_3'(A_1102,B_1103,C_1104),C_1104)
      | ( set_difference(A_1102,B_1103) = C_1104 ) ),
    inference(resolution,[status(thm)],[c_18821,c_24]) ).

tff(c_23439,plain,
    ! [C_1105,A_1106,B_1107] :
      ( ~ empty(C_1105)
      | ~ subset(A_1106,B_1107)
      | ( set_difference(A_1106,B_1107) = C_1105 ) ),
    inference(resolution,[status(thm)],[c_23349,c_62]) ).

tff(c_23696,plain,
    ! [A_1112,B_1113] :
      ( ~ subset(A_1112,B_1113)
      | ( set_difference(A_1112,B_1113) = '#skF_8' ) ),
    inference(resolution,[status(thm)],[c_42,c_23439]) ).

tff(c_23729,plain,
    set_difference('#skF_4','#skF_5') = '#skF_8',
    inference(resolution,[status(thm)],[c_9759,c_23696]) ).

tff(c_23747,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9775,c_23729]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU131+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n028.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 11:54:24 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 13.26/4.31  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.26/4.32  
% 13.26/4.32  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.43/4.35  
% 13.43/4.35  Inference rules
% 13.43/4.35  ----------------------
% 13.43/4.35  #Ref     : 0
% 13.43/4.35  #Sup     : 5688
% 13.43/4.35  #Fact    : 0
% 13.43/4.35  #Define  : 0
% 13.43/4.35  #Split   : 13
% 13.43/4.35  #Chain   : 0
% 13.43/4.35  #Close   : 0
% 13.43/4.35  
% 13.43/4.35  Ordering : KBO
% 13.43/4.35  
% 13.43/4.35  Simplification rules
% 13.43/4.35  ----------------------
% 13.43/4.35  #Subsume      : 2399
% 13.43/4.35  #Demod        : 1481
% 13.43/4.35  #Tautology    : 648
% 13.43/4.35  #SimpNegUnit  : 11
% 13.43/4.35  #BackRed      : 12
% 13.43/4.35  
% 13.43/4.35  #Partial instantiations: 0
% 13.43/4.35  #Strategies tried      : 1
% 13.43/4.35  
% 13.43/4.35  Timing (in seconds)
% 13.43/4.35  ----------------------
% 13.43/4.36  Preprocessing        : 0.50
% 13.43/4.36  Parsing              : 0.25
% 13.43/4.36  CNF conversion       : 0.04
% 13.43/4.36  Main loop            : 2.79
% 13.43/4.36  Inferencing          : 0.94
% 13.43/4.36  Reduction            : 0.63
% 13.43/4.36  Demodulation         : 0.42
% 13.43/4.36  BG Simplification    : 0.08
% 13.43/4.36  Subsumption          : 0.94
% 13.43/4.36  Abstraction          : 0.10
% 13.43/4.36  MUC search           : 0.00
% 13.43/4.36  Cooper               : 0.00
% 13.43/4.36  Total                : 3.34
% 13.43/4.36  Index Insertion      : 0.00
% 13.43/4.36  Index Deletion       : 0.00
% 13.43/4.36  Index Matching       : 0.00
% 13.43/4.36  BG Taut test         : 0.00
%------------------------------------------------------------------------------