TSTP Solution File: SEU141+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU141+2 : 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 : n016.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 10:57:43 EDT 2023

% Result   : Theorem 37.20s 24.84s
% Output   : CNFRefutation 37.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  156 (  82 unt;  27 typ;   0 def)
%            Number of atoms       :  179 ( 110 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  107 (  57   ~;  39   |;   3   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   44 (  20   >;  24   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;   7 con; 0-3 aty)
%            Number of variables   :  186 (; 184   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > set_union2 > set_intersection2 > set_difference > #nlpp > empty_set > #skF_11 > #skF_18 > #skF_17 > #skF_6 > #skF_15 > #skF_1 > #skF_13 > #skF_10 > #skF_16 > #skF_14 > #skF_12 > #skF_5 > #skF_2 > #skF_9 > #skF_7 > #skF_3 > #skF_8 > #skF_4

%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_18',type,
    '#skF_18': $i ).

tff('#skF_17',type,
    '#skF_17': $i ).

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

tff('#skF_15',type,
    '#skF_15': $i ).

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

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

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

tff('#skF_16',type,
    '#skF_16': $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i ) > $i ).

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

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

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

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

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

tff(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

tff(f_40,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(f_125,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_248,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_91,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> ( set_intersection2(A,B) = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

tff(f_260,negated_conjecture,
    ~ ! [A,B] :
        ( disjoint(A,B)
      <=> ( set_difference(A,B) = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).

tff(f_130,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_183,lemma,
    ! [A,B] :
      ( ( set_difference(A,B) = empty_set )
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

tff(f_211,lemma,
    ! [A,B] : ( set_difference(set_union2(A,B),B) = set_difference(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).

tff(f_38,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_179,lemma,
    ! [A,B] : subset(set_difference(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).

tff(f_185,lemma,
    ! [A,B] : ( set_union2(A,set_difference(B,A)) = set_union2(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).

tff(f_215,lemma,
    ! [A,B] :
      ( subset(A,B)
     => ( B = set_union2(A,set_difference(B,A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).

tff(f_68,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_116,axiom,
    ! [A,B] : ( set_intersection2(A,A) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

tff(f_233,lemma,
    ! [A,B] :
      ( ~ ( ~ disjoint(A,B)
          & ! [C] : ~ in(C,set_intersection2(A,B)) )
      & ~ ( ? [C] : in(C,set_intersection2(A,B))
          & disjoint(A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

tff(f_255,lemma,
    ! [A,B] : subset(A,set_union2(A,B)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

tff(f_162,lemma,
    ! [A,B] :
      ( subset(A,B)
     => ( set_intersection2(A,B) = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

tff(f_217,lemma,
    ! [A,B] : ( set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).

tff(c_8,plain,
    ! [B_8,A_7] : ( set_intersection2(B_8,A_7) = set_intersection2(A_7,B_8) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_114,plain,
    empty('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_215,plain,
    ! [A_127] :
      ( ( empty_set = A_127 )
      | ~ empty(A_127) ),
    inference(cnfTransformation,[status(thm)],[f_248]) ).

tff(c_224,plain,
    empty_set = '#skF_9',
    inference(resolution,[status(thm)],[c_114,c_215]) ).

tff(c_82,plain,
    ! [A_38,B_39] :
      ( disjoint(A_38,B_39)
      | ( set_intersection2(A_38,B_39) != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_86545,plain,
    ! [A_1788,B_1789] :
      ( disjoint(A_1788,B_1789)
      | ( set_intersection2(A_1788,B_1789) != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_82]) ).

tff(c_194,plain,
    ( ~ disjoint('#skF_15','#skF_16')
    | disjoint('#skF_17','#skF_18') ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_225,plain,
    ~ disjoint('#skF_15','#skF_16'),
    inference(splitLeft,[status(thm)],[c_194]) ).

tff(c_86556,plain,
    set_intersection2('#skF_15','#skF_16') != '#skF_9',
    inference(resolution,[status(thm)],[c_86545,c_225]) ).

tff(c_86561,plain,
    set_intersection2('#skF_16','#skF_15') != '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_86556]) ).

tff(c_118,plain,
    ! [A_54] : subset(A_54,A_54),
    inference(cnfTransformation,[status(thm)],[f_130]) ).

tff(c_154,plain,
    ! [A_84,B_85] :
      ( ( set_difference(A_84,B_85) = empty_set )
      | ~ subset(A_84,B_85) ),
    inference(cnfTransformation,[status(thm)],[f_183]) ).

tff(c_86427,plain,
    ! [A_1783,B_1784] :
      ( ( set_difference(A_1783,B_1784) = '#skF_9' )
      | ~ subset(A_1783,B_1784) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_154]) ).

tff(c_86460,plain,
    ! [A_54] : ( set_difference(A_54,A_54) = '#skF_9' ),
    inference(resolution,[status(thm)],[c_118,c_86427]) ).

tff(c_85595,plain,
    ! [A_1728,B_1729] :
      ( disjoint(A_1728,B_1729)
      | ( set_intersection2(A_1728,B_1729) != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_82]) ).

tff(c_85603,plain,
    set_intersection2('#skF_15','#skF_16') != '#skF_9',
    inference(resolution,[status(thm)],[c_85595,c_225]) ).

tff(c_85607,plain,
    set_intersection2('#skF_16','#skF_15') != '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_85603]) ).

tff(c_85527,plain,
    ! [A_1725,B_1726] :
      ( ( set_difference(A_1725,B_1726) = '#skF_9' )
      | ~ subset(A_1725,B_1726) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_154]) ).

tff(c_85560,plain,
    ! [A_54] : ( set_difference(A_54,A_54) = '#skF_9' ),
    inference(resolution,[status(thm)],[c_118,c_85527]) ).

tff(c_192,plain,
    ( ( set_difference('#skF_15','#skF_16') = '#skF_15' )
    | ( set_difference('#skF_17','#skF_18') != '#skF_17' ) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_628,plain,
    set_difference('#skF_17','#skF_18') != '#skF_17',
    inference(splitLeft,[status(thm)],[c_192]) ).

tff(c_168,plain,
    ! [A_95,B_96] : ( set_difference(set_union2(A_95,B_96),B_96) = set_difference(A_95,B_96) ),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_6,plain,
    ! [B_6,A_5] : ( set_union2(B_6,A_5) = set_union2(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_150,plain,
    ! [A_82,B_83] : subset(set_difference(A_82,B_83),A_82),
    inference(cnfTransformation,[status(thm)],[f_179]) ).

tff(c_156,plain,
    ! [A_86,B_87] : ( set_union2(A_86,set_difference(B_87,A_86)) = set_union2(A_86,B_87) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_170,plain,
    ! [A_97,B_98] :
      ( ( set_union2(A_97,set_difference(B_98,A_97)) = B_98 )
      | ~ subset(A_97,B_98) ),
    inference(cnfTransformation,[status(thm)],[f_215]) ).

tff(c_1320,plain,
    ! [A_209,B_210] :
      ( ( set_union2(A_209,B_210) = B_210 )
      | ~ subset(A_209,B_210) ),
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_170]) ).

tff(c_1359,plain,
    ! [A_211,B_212] : ( set_union2(set_difference(A_211,B_212),A_211) = A_211 ),
    inference(resolution,[status(thm)],[c_150,c_1320]) ).

tff(c_1422,plain,
    ! [A_5,B_212] : ( set_union2(A_5,set_difference(A_5,B_212)) = A_5 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_1359]) ).

tff(c_2168,plain,
    ! [A_239,B_240] :
      ( in('#skF_4'(A_239,B_240),A_239)
      | subset(A_239,B_240) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_106,plain,
    ! [A_48] : ( set_intersection2(A_48,A_48) = A_48 ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_966,plain,
    ! [A_38,B_39] :
      ( disjoint(A_38,B_39)
      | ( set_intersection2(A_38,B_39) != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_82]) ).

tff(c_1988,plain,
    ! [A_228,B_229,C_230] :
      ( ~ disjoint(A_228,B_229)
      | ~ in(C_230,set_intersection2(A_228,B_229)) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_2025,plain,
    ! [A_231,C_232] :
      ( ~ disjoint(A_231,A_231)
      | ~ in(C_232,A_231) ),
    inference(superposition,[status(thm),theory(equality)],[c_106,c_1988]) ).

tff(c_2028,plain,
    ! [C_232,B_39] :
      ( ~ in(C_232,B_39)
      | ( set_intersection2(B_39,B_39) != '#skF_9' ) ),
    inference(resolution,[status(thm)],[c_966,c_2025]) ).

tff(c_2030,plain,
    ! [C_232,B_39] :
      ( ~ in(C_232,B_39)
      | ( B_39 != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_2028]) ).

tff(c_2224,plain,
    ! [A_245,B_246] :
      ( ( A_245 != '#skF_9' )
      | subset(A_245,B_246) ),
    inference(resolution,[status(thm)],[c_2168,c_2030]) ).

tff(c_201,plain,
    ! [A_97,B_98] :
      ( ( set_union2(A_97,B_98) = B_98 )
      | ~ subset(A_97,B_98) ),
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_170]) ).

tff(c_3419,plain,
    ! [A_306,B_307] :
      ( ( set_union2(A_306,B_307) = B_307 )
      | ( A_306 != '#skF_9' ) ),
    inference(resolution,[status(thm)],[c_2224,c_201]) ).

tff(c_3515,plain,
    ! [A_5,B_212] :
      ( ( set_difference(A_5,B_212) = A_5 )
      | ( A_5 != '#skF_9' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1422,c_3419]) ).

tff(c_188,plain,
    ! [A_115,B_116] : subset(A_115,set_union2(A_115,B_116)),
    inference(cnfTransformation,[status(thm)],[f_255]) ).

tff(c_754,plain,
    ! [A_177,B_178] :
      ( ( set_intersection2(A_177,B_178) = A_177 )
      | ~ subset(A_177,B_178) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_783,plain,
    ! [A_115,B_116] : ( set_intersection2(A_115,set_union2(A_115,B_116)) = A_115 ),
    inference(resolution,[status(thm)],[c_188,c_754]) ).

tff(c_2757,plain,
    ! [A_286,B_287] : ( set_difference(set_union2(A_286,B_287),B_287) = set_difference(A_286,B_287) ),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_30211,plain,
    ! [A_930,B_931] : ( set_difference(set_union2(A_930,B_931),A_930) = set_difference(B_931,A_930) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_2757]) ).

tff(c_172,plain,
    ! [A_99,B_100] : ( set_difference(A_99,set_difference(A_99,B_100)) = set_intersection2(A_99,B_100) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_30321,plain,
    ! [A_930,B_931] : ( set_difference(set_union2(A_930,B_931),set_difference(B_931,A_930)) = set_intersection2(set_union2(A_930,B_931),A_930) ),
    inference(superposition,[status(thm),theory(equality)],[c_30211,c_172]) ).

tff(c_49710,plain,
    ! [A_1207,B_1208] : ( set_difference(set_union2(A_1207,B_1208),set_difference(B_1208,A_1207)) = A_1207 ),
    inference(demodulation,[status(thm),theory(equality)],[c_783,c_8,c_30321]) ).

tff(c_49877,plain,
    ! [B_212,A_5] :
      ( ( set_difference(set_union2(B_212,A_5),A_5) = B_212 )
      | ( A_5 != '#skF_9' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3515,c_49710]) ).

tff(c_49987,plain,
    ! [B_212] : ( set_difference(B_212,'#skF_9') = B_212 ),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_49877]) ).

tff(c_196,plain,
    ( ( set_difference('#skF_15','#skF_16') = '#skF_15' )
    | disjoint('#skF_17','#skF_18') ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_417,plain,
    disjoint('#skF_17','#skF_18'),
    inference(splitLeft,[status(thm)],[c_196]) ).

tff(c_80,plain,
    ! [A_38,B_39] :
      ( ( set_intersection2(A_38,B_39) = empty_set )
      | ~ disjoint(A_38,B_39) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_838,plain,
    ! [A_185,B_186] :
      ( ( set_intersection2(A_185,B_186) = '#skF_9' )
      | ~ disjoint(A_185,B_186) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_80]) ).

tff(c_846,plain,
    set_intersection2('#skF_17','#skF_18') = '#skF_9',
    inference(resolution,[status(thm)],[c_417,c_838]) ).

tff(c_28488,plain,
    ! [A_915,B_916] : ( set_intersection2(set_difference(A_915,B_916),A_915) = set_difference(A_915,B_916) ),
    inference(resolution,[status(thm)],[c_150,c_754]) ).

tff(c_28933,plain,
    ! [A_7,B_916] : ( set_intersection2(A_7,set_difference(A_7,B_916)) = set_difference(A_7,B_916) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_28488]) ).

tff(c_1608,plain,
    ! [A_217,B_218] : ( set_difference(A_217,set_difference(A_217,B_218)) = set_intersection2(A_217,B_218) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_1611,plain,
    ! [A_217,B_218] : ( set_intersection2(A_217,set_difference(A_217,B_218)) = set_difference(A_217,set_intersection2(A_217,B_218)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1608,c_172]) ).

tff(c_84298,plain,
    ! [A_1689,B_1690] : ( set_difference(A_1689,set_intersection2(A_1689,B_1690)) = set_difference(A_1689,B_1690) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28933,c_1611]) ).

tff(c_85027,plain,
    set_difference('#skF_17','#skF_18') = set_difference('#skF_17','#skF_9'),
    inference(superposition,[status(thm),theory(equality)],[c_846,c_84298]) ).

tff(c_85163,plain,
    set_difference('#skF_17','#skF_18') = '#skF_17',
    inference(demodulation,[status(thm),theory(equality)],[c_49987,c_85027]) ).

tff(c_85165,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_628,c_85163]) ).

tff(c_85166,plain,
    set_difference('#skF_15','#skF_16') = '#skF_15',
    inference(splitRight,[status(thm)],[c_192]) ).

tff(c_85877,plain,
    ! [A_1741,B_1742] : ( set_difference(A_1741,set_difference(A_1741,B_1742)) = set_intersection2(A_1741,B_1742) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_85920,plain,
    set_intersection2('#skF_15','#skF_16') = set_difference('#skF_15','#skF_15'),
    inference(superposition,[status(thm),theory(equality)],[c_85166,c_85877]) ).

tff(c_85941,plain,
    set_intersection2('#skF_15','#skF_16') = '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_85560,c_85920]) ).

tff(c_85963,plain,
    set_intersection2('#skF_16','#skF_15') = '#skF_9',
    inference(superposition,[status(thm),theory(equality)],[c_85941,c_8]) ).

tff(c_85982,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_85607,c_85963]) ).

tff(c_85983,plain,
    set_difference('#skF_15','#skF_16') = '#skF_15',
    inference(splitRight,[status(thm)],[c_196]) ).

tff(c_86737,plain,
    ! [A_1799,B_1800] : ( set_difference(A_1799,set_difference(A_1799,B_1800)) = set_intersection2(A_1799,B_1800) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_86771,plain,
    set_intersection2('#skF_15','#skF_16') = set_difference('#skF_15','#skF_15'),
    inference(superposition,[status(thm),theory(equality)],[c_85983,c_86737]) ).

tff(c_86789,plain,
    set_intersection2('#skF_15','#skF_16') = '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_86460,c_86771]) ).

tff(c_86805,plain,
    set_intersection2('#skF_16','#skF_15') = '#skF_9',
    inference(superposition,[status(thm),theory(equality)],[c_86789,c_8]) ).

tff(c_86822,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_86561,c_86805]) ).

tff(c_86824,plain,
    disjoint('#skF_15','#skF_16'),
    inference(splitRight,[status(thm)],[c_194]) ).

tff(c_190,plain,
    ( ~ disjoint('#skF_15','#skF_16')
    | ( set_difference('#skF_17','#skF_18') != '#skF_17' ) ),
    inference(cnfTransformation,[status(thm)],[f_260]) ).

tff(c_86874,plain,
    set_difference('#skF_17','#skF_18') != '#skF_17',
    inference(demodulation,[status(thm),theory(equality)],[c_86824,c_190]) ).

tff(c_42,plain,
    ! [A_21,B_22] :
      ( in('#skF_4'(A_21,B_22),A_21)
      | subset(A_21,B_22) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_87925,plain,
    ! [A_38,B_39] :
      ( disjoint(A_38,B_39)
      | ( set_intersection2(A_38,B_39) != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_82]) ).

tff(c_89268,plain,
    ! [A_1941,B_1942,C_1943] :
      ( ~ disjoint(A_1941,B_1942)
      | ~ in(C_1943,set_intersection2(A_1941,B_1942)) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_89329,plain,
    ! [A_1944,C_1945] :
      ( ~ disjoint(A_1944,A_1944)
      | ~ in(C_1945,A_1944) ),
    inference(superposition,[status(thm),theory(equality)],[c_106,c_89268]) ).

tff(c_89344,plain,
    ! [C_1945,B_39] :
      ( ~ in(C_1945,B_39)
      | ( set_intersection2(B_39,B_39) != '#skF_9' ) ),
    inference(resolution,[status(thm)],[c_87925,c_89329]) ).

tff(c_89352,plain,
    ! [C_1946,B_1947] :
      ( ~ in(C_1946,B_1947)
      | ( B_1947 != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_89344]) ).

tff(c_89435,plain,
    ! [A_1953,B_1954] :
      ( ( A_1953 != '#skF_9' )
      | subset(A_1953,B_1954) ),
    inference(resolution,[status(thm)],[c_42,c_89352]) ).

tff(c_89701,plain,
    ! [A_1969,B_1970] :
      ( ( set_union2(A_1969,B_1970) = B_1970 )
      | ( A_1969 != '#skF_9' ) ),
    inference(resolution,[status(thm)],[c_89435,c_201]) ).

tff(c_88086,plain,
    ! [A_1884,B_1885] :
      ( ( set_union2(A_1884,B_1885) = B_1885 )
      | ~ subset(A_1884,B_1885) ),
    inference(demodulation,[status(thm),theory(equality)],[c_156,c_170]) ).

tff(c_88235,plain,
    ! [A_1888,B_1889] : ( set_union2(set_difference(A_1888,B_1889),A_1888) = A_1888 ),
    inference(resolution,[status(thm)],[c_150,c_88086]) ).

tff(c_88307,plain,
    ! [A_5,B_1889] : ( set_union2(A_5,set_difference(A_5,B_1889)) = A_5 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_88235]) ).

tff(c_89725,plain,
    ! [A_1969,B_1889] :
      ( ( set_difference(A_1969,B_1889) = A_1969 )
      | ( A_1969 != '#skF_9' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_89701,c_88307]) ).

tff(c_89527,plain,
    ! [A_1962,B_1963] : ( set_difference(set_union2(A_1962,B_1963),B_1963) = set_difference(A_1962,B_1963) ),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_89585,plain,
    ! [B_6,A_5] : ( set_difference(set_union2(B_6,A_5),B_6) = set_difference(A_5,B_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_89527]) ).

tff(c_87425,plain,
    ! [A_1858,B_1859] :
      ( ( set_intersection2(A_1858,B_1859) = A_1858 )
      | ~ subset(A_1858,B_1859) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_87454,plain,
    ! [A_115,B_116] : ( set_intersection2(A_115,set_union2(A_115,B_116)) = A_115 ),
    inference(resolution,[status(thm)],[c_188,c_87425]) ).

tff(c_88119,plain,
    ! [A_115,B_116] : ( set_union2(A_115,set_union2(A_115,B_116)) = set_union2(A_115,B_116) ),
    inference(resolution,[status(thm)],[c_188,c_88086]) ).

tff(c_90404,plain,
    ! [A_1981,B_1982] : ( set_union2(A_1981,set_difference(B_1982,A_1981)) = set_union2(A_1981,B_1982) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_139954,plain,
    ! [A_2948,B_2949] : ( set_difference(set_union2(A_2948,B_2949),set_difference(B_2949,A_2948)) = set_difference(A_2948,set_difference(B_2949,A_2948)) ),
    inference(superposition,[status(thm),theory(equality)],[c_90404,c_168]) ).

tff(c_140103,plain,
    ! [A_115,B_116] : ( set_difference(set_union2(A_115,B_116),set_difference(set_union2(A_115,B_116),A_115)) = set_difference(A_115,set_difference(set_union2(A_115,B_116),A_115)) ),
    inference(superposition,[status(thm),theory(equality)],[c_88119,c_139954]) ).

tff(c_140220,plain,
    ! [A_2950,B_2951] : ( set_difference(A_2950,set_difference(B_2951,A_2950)) = A_2950 ),
    inference(demodulation,[status(thm),theory(equality)],[c_89585,c_87454,c_8,c_172,c_140103]) ).

tff(c_142792,plain,
    ! [B_1889] : ( set_difference(B_1889,'#skF_9') = B_1889 ),
    inference(superposition,[status(thm),theory(equality)],[c_89725,c_140220]) ).

tff(c_86823,plain,
    disjoint('#skF_17','#skF_18'),
    inference(splitRight,[status(thm)],[c_194]) ).

tff(c_87513,plain,
    ! [A_1863,B_1864] :
      ( ( set_intersection2(A_1863,B_1864) = '#skF_9' )
      | ~ disjoint(A_1863,B_1864) ),
    inference(demodulation,[status(thm),theory(equality)],[c_224,c_80]) ).

tff(c_87529,plain,
    set_intersection2('#skF_17','#skF_18') = '#skF_9',
    inference(resolution,[status(thm)],[c_86823,c_87513]) ).

tff(c_103781,plain,
    ! [A_2296,B_2297] : ( set_intersection2(set_difference(A_2296,B_2297),A_2296) = set_difference(A_2296,B_2297) ),
    inference(resolution,[status(thm)],[c_150,c_87425]) ).

tff(c_103967,plain,
    ! [A_2296,B_2297] : ( set_intersection2(A_2296,set_difference(A_2296,B_2297)) = set_difference(A_2296,B_2297) ),
    inference(superposition,[status(thm),theory(equality)],[c_103781,c_8]) ).

tff(c_88455,plain,
    ! [A_1892,B_1893] : ( set_difference(A_1892,set_difference(A_1892,B_1893)) = set_intersection2(A_1892,B_1893) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_88458,plain,
    ! [A_1892,B_1893] : ( set_intersection2(A_1892,set_difference(A_1892,B_1893)) = set_difference(A_1892,set_intersection2(A_1892,B_1893)) ),
    inference(superposition,[status(thm),theory(equality)],[c_88455,c_172]) ).

tff(c_170654,plain,
    ! [A_3347,B_3348] : ( set_difference(A_3347,set_intersection2(A_3347,B_3348)) = set_difference(A_3347,B_3348) ),
    inference(demodulation,[status(thm),theory(equality)],[c_103967,c_88458]) ).

tff(c_171466,plain,
    set_difference('#skF_17','#skF_18') = set_difference('#skF_17','#skF_9'),
    inference(superposition,[status(thm),theory(equality)],[c_87529,c_170654]) ).

tff(c_171661,plain,
    set_difference('#skF_17','#skF_18') = '#skF_17',
    inference(demodulation,[status(thm),theory(equality)],[c_142792,c_171466]) ).

tff(c_171663,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_86874,c_171661]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU141+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % 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
% 0.17/0.35  % Computer : n016.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 12:07:22 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 37.20/24.84  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.41/24.86  
% 37.41/24.86  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.63/24.90  
% 37.63/24.90  Inference rules
% 37.63/24.90  ----------------------
% 37.63/24.90  #Ref     : 2
% 37.63/24.90  #Sup     : 42819
% 37.63/24.90  #Fact    : 12
% 37.63/24.90  #Define  : 0
% 37.63/24.90  #Split   : 19
% 37.63/24.90  #Chain   : 0
% 37.63/24.90  #Close   : 0
% 37.63/24.90  
% 37.63/24.90  Ordering : KBO
% 37.63/24.90  
% 37.63/24.90  Simplification rules
% 37.63/24.90  ----------------------
% 37.63/24.90  #Subsume      : 14264
% 37.63/24.90  #Demod        : 21848
% 37.63/24.90  #Tautology    : 16171
% 37.63/24.90  #SimpNegUnit  : 638
% 37.63/24.90  #BackRed      : 17
% 37.63/24.90  
% 37.63/24.90  #Partial instantiations: 0
% 37.63/24.90  #Strategies tried      : 1
% 37.63/24.90  
% 37.63/24.90  Timing (in seconds)
% 37.63/24.90  ----------------------
% 37.63/24.90  Preprocessing        : 0.64
% 37.63/24.90  Parsing              : 0.32
% 37.63/24.90  CNF conversion       : 0.06
% 37.63/24.90  Main loop            : 23.13
% 37.63/24.90  Inferencing          : 3.00
% 37.63/24.90  Reduction            : 11.59
% 37.63/24.90  Demodulation         : 9.16
% 37.63/24.90  BG Simplification    : 0.16
% 37.63/24.90  Subsumption          : 6.65
% 37.63/24.90  Abstraction          : 0.23
% 37.63/24.90  MUC search           : 0.00
% 37.63/24.90  Cooper               : 0.00
% 37.63/24.90  Total                : 23.84
% 37.63/24.90  Index Insertion      : 0.00
% 37.63/24.90  Index Deletion       : 0.00
% 37.63/24.90  Index Matching       : 0.00
% 37.63/24.90  BG Taut test         : 0.00
%------------------------------------------------------------------------------