TSTP Solution File: SEU053+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU053+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 : n025.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 10:57:32 EDT 2023

% Result   : Theorem 28.54s 15.42s
% Output   : CNFRefutation 28.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   47
% Syntax   : Number of formulae    :  108 (  28 unt;  33 typ;   0 def)
%            Number of atoms       :  162 (  62 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  143 (  56   ~;  66   |;   7   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  23   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;  10 con; 0-2 aty)
%            Number of variables   :   85 (;  84   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > disjoint_nonempty > disjoint > relation_empty_yielding > relation > one_to_one > function > empty > set_intersection2 > relation_image > apply > #nlpp > singleton > relation_dom > powerset > empty_set > #skF_5 > #skF_4 > #skF_11 > #skF_15 > #skF_8 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_3 > #skF_2 > #skF_12 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_220,negated_conjecture,
    ~ ! [A] :
        ( ( relation(A)
          & function(A) )
       => ( ! [B,C] : ( relation_image(A,set_intersection2(B,C)) = set_intersection2(relation_image(A,B),relation_image(A,C)) )
         => one_to_one(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_funct_1) ).

tff(f_79,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
      <=> ! [B,C] :
            ( ( in(B,relation_dom(A))
              & in(C,relation_dom(A))
              & ( apply(A,B) = apply(A,C) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).

tff(f_119,axiom,
    ! [A,B] : ( set_intersection2(A,A) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

tff(f_147,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_262,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_64,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> ( set_intersection2(A,B) = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

tff(f_186,axiom,
    ! [A,B] :
      ( ( ~ empty(A)
        & ~ empty(B) )
     => ( disjoint_nonempty(A,B)
      <=> disjoint(A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_subset_1) ).

tff(f_128,axiom,
    ! [A,B] :
      ( ( ~ empty(A)
        & ~ empty(B) )
     => ~ disjoint_nonempty(A,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r1_subset_1) ).

tff(f_100,axiom,
    ! [A] : ~ empty(singleton(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).

tff(f_210,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ( in(A,relation_dom(B))
       => ( relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).

tff(f_224,axiom,
    ! [A] :
      ( relation(A)
     => ( relation_image(A,empty_set) = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).

tff(f_229,axiom,
    ! [A,B] :
      ( ( A != B )
     => disjoint(singleton(A),singleton(B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).

tff(f_53,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(f_96,axiom,
    ! [A] : ~ empty(powerset(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

tff(c_124,plain,
    ~ one_to_one('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_220]) ).

tff(c_128,plain,
    function('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_220]) ).

tff(c_130,plain,
    relation('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_220]) ).

tff(c_1292,plain,
    ! [A_181] :
      ( ( '#skF_4'(A_181) != '#skF_3'(A_181) )
      | one_to_one(A_181)
      | ~ function(A_181)
      | ~ relation(A_181) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_1322,plain,
    ( ( '#skF_4'('#skF_16') != '#skF_3'('#skF_16') )
    | one_to_one('#skF_16')
    | ~ function('#skF_16') ),
    inference(resolution,[status(thm)],[c_130,c_1292]) ).

tff(c_1340,plain,
    ( ( '#skF_4'('#skF_16') != '#skF_3'('#skF_16') )
    | one_to_one('#skF_16') ),
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_1322]) ).

tff(c_1341,plain,
    '#skF_4'('#skF_16') != '#skF_3'('#skF_16'),
    inference(negUnitSimplification,[status(thm)],[c_124,c_1340]) ).

tff(c_68,plain,
    ! [A_30] : ( set_intersection2(A_30,A_30) = A_30 ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_84,plain,
    empty('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_171,plain,
    ! [A_79] :
      ( ( empty_set = A_79 )
      | ~ empty(A_79) ),
    inference(cnfTransformation,[status(thm)],[f_262]) ).

tff(c_190,plain,
    empty_set = '#skF_9',
    inference(resolution,[status(thm)],[c_84,c_171]) ).

tff(c_30,plain,
    ! [A_13,B_14] :
      ( disjoint(A_13,B_14)
      | ( set_intersection2(A_13,B_14) != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_646,plain,
    ! [A_13,B_14] :
      ( disjoint(A_13,B_14)
      | ( set_intersection2(A_13,B_14) != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_30]) ).

tff(c_1057,plain,
    ! [A_167,B_168] :
      ( disjoint_nonempty(A_167,B_168)
      | ~ disjoint(A_167,B_168)
      | empty(B_168)
      | empty(A_167) ),
    inference(cnfTransformation,[status(thm)],[f_186]) ).

tff(c_70,plain,
    ! [A_32,B_33] :
      ( ~ disjoint_nonempty(A_32,A_32)
      | empty(B_33)
      | empty(A_32) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_760,plain,
    ! [A_32] :
      ( ~ disjoint_nonempty(A_32,A_32)
      | empty(A_32) ),
    inference(splitLeft,[status(thm)],[c_70]) ).

tff(c_1063,plain,
    ! [B_169] :
      ( ~ disjoint(B_169,B_169)
      | empty(B_169) ),
    inference(resolution,[status(thm)],[c_1057,c_760]) ).

tff(c_1075,plain,
    ! [B_14] :
      ( empty(B_14)
      | ( set_intersection2(B_14,B_14) != '#skF_9' ) ),
    inference(resolution,[status(thm)],[c_646,c_1063]) ).

tff(c_1086,plain,
    ! [B_170] :
      ( empty(B_170)
      | ( B_170 != '#skF_9' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_1075]) ).

tff(c_56,plain,
    ! [A_27] : ~ empty(singleton(A_27)),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_1137,plain,
    ! [A_27] : ( singleton(A_27) != '#skF_9' ),
    inference(resolution,[status(thm)],[c_1086,c_56]) ).

tff(c_40,plain,
    ! [A_15] :
      ( in('#skF_3'(A_15),relation_dom(A_15))
      | one_to_one(A_15)
      | ~ function(A_15)
      | ~ relation(A_15) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_5394,plain,
    ! [B_3722,A_3723] :
      ( ( relation_image(B_3722,singleton(A_3723)) = singleton(apply(B_3722,A_3723)) )
      | ~ in(A_3723,relation_dom(B_3722))
      | ~ function(B_3722)
      | ~ relation(B_3722) ),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_5493,plain,
    ! [A_15] :
      ( ( relation_image(A_15,singleton('#skF_3'(A_15))) = singleton(apply(A_15,'#skF_3'(A_15))) )
      | one_to_one(A_15)
      | ~ function(A_15)
      | ~ relation(A_15) ),
    inference(resolution,[status(thm)],[c_40,c_5394]) ).

tff(c_22613,plain,
    ! [A_5732] :
      ( ( relation_image(A_5732,singleton('#skF_3'(A_5732))) = singleton(apply(A_5732,'#skF_3'(A_5732))) )
      | one_to_one(A_5732)
      | ~ function(A_5732)
      | ~ relation(A_5732) ),
    inference(resolution,[status(thm)],[c_40,c_5394]) ).

tff(c_126,plain,
    ! [B_50,C_51] : ( set_intersection2(relation_image('#skF_16',B_50),relation_image('#skF_16',C_51)) = relation_image('#skF_16',set_intersection2(B_50,C_51)) ),
    inference(cnfTransformation,[status(thm)],[f_220]) ).

tff(c_22652,plain,
    ! [B_50] :
      ( ( set_intersection2(relation_image('#skF_16',B_50),singleton(apply('#skF_16','#skF_3'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_50,singleton('#skF_3'('#skF_16')))) )
      | one_to_one('#skF_16')
      | ~ function('#skF_16')
      | ~ relation('#skF_16') ),
    inference(superposition,[status(thm),theory(equality)],[c_22613,c_126]) ).

tff(c_22784,plain,
    ! [B_50] :
      ( ( set_intersection2(relation_image('#skF_16',B_50),singleton(apply('#skF_16','#skF_3'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_50,singleton('#skF_3'('#skF_16')))) )
      | one_to_one('#skF_16') ),
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_128,c_22652]) ).

tff(c_23187,plain,
    ! [B_5811] : ( set_intersection2(relation_image('#skF_16',B_5811),singleton(apply('#skF_16','#skF_3'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_5811,singleton('#skF_3'('#skF_16')))) ),
    inference(negUnitSimplification,[status(thm)],[c_124,c_22784]) ).

tff(c_23271,plain,
    ( ( set_intersection2(singleton(apply('#skF_16','#skF_3'('#skF_16'))),singleton(apply('#skF_16','#skF_3'('#skF_16')))) = relation_image('#skF_16',set_intersection2(singleton('#skF_3'('#skF_16')),singleton('#skF_3'('#skF_16')))) )
    | one_to_one('#skF_16')
    | ~ function('#skF_16')
    | ~ relation('#skF_16') ),
    inference(superposition,[status(thm),theory(equality)],[c_5493,c_23187]) ).

tff(c_23439,plain,
    ( ( relation_image('#skF_16',singleton('#skF_3'('#skF_16'))) = singleton(apply('#skF_16','#skF_3'('#skF_16'))) )
    | one_to_one('#skF_16') ),
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_128,c_68,c_68,c_23271]) ).

tff(c_23440,plain,
    relation_image('#skF_16',singleton('#skF_3'('#skF_16'))) = singleton(apply('#skF_16','#skF_3'('#skF_16'))),
    inference(negUnitSimplification,[status(thm)],[c_124,c_23439]) ).

tff(c_132,plain,
    ! [A_52] :
      ( ( relation_image(A_52,empty_set) = empty_set )
      | ~ relation(A_52) ),
    inference(cnfTransformation,[status(thm)],[f_224]) ).

tff(c_322,plain,
    ! [A_97] :
      ( ( relation_image(A_97,'#skF_9') = '#skF_9' )
      | ~ relation(A_97) ),
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_190,c_132]) ).

tff(c_354,plain,
    relation_image('#skF_16','#skF_9') = '#skF_9',
    inference(resolution,[status(thm)],[c_130,c_322]) ).

tff(c_134,plain,
    ! [A_53,B_54] :
      ( disjoint(singleton(A_53),singleton(B_54))
      | ( B_54 = A_53 ) ),
    inference(cnfTransformation,[status(thm)],[f_229]) ).

tff(c_28,plain,
    ! [A_13,B_14] :
      ( ( set_intersection2(A_13,B_14) = empty_set )
      | ~ disjoint(A_13,B_14) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_769,plain,
    ! [A_132,B_133] :
      ( ( set_intersection2(A_132,B_133) = '#skF_9' )
      | ~ disjoint(A_132,B_133) ),
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_28]) ).

tff(c_1006,plain,
    ! [A_163,B_164] :
      ( ( set_intersection2(singleton(A_163),singleton(B_164)) = '#skF_9' )
      | ( B_164 = A_163 ) ),
    inference(resolution,[status(thm)],[c_134,c_769]) ).

tff(c_418,plain,
    ! [B_109,A_110] : ( set_intersection2(B_109,A_110) = set_intersection2(A_110,B_109) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_524,plain,
    ! [C_112,B_113] : ( set_intersection2(relation_image('#skF_16',C_112),relation_image('#skF_16',B_113)) = relation_image('#skF_16',set_intersection2(B_113,C_112)) ),
    inference(superposition,[status(thm),theory(equality)],[c_418,c_126]) ).

tff(c_540,plain,
    ! [C_112,B_113] : ( relation_image('#skF_16',set_intersection2(C_112,B_113)) = relation_image('#skF_16',set_intersection2(B_113,C_112)) ),
    inference(superposition,[status(thm),theory(equality)],[c_524,c_126]) ).

tff(c_1018,plain,
    ! [B_164,A_163] :
      ( ( relation_image('#skF_16',set_intersection2(singleton(B_164),singleton(A_163))) = relation_image('#skF_16','#skF_9') )
      | ( B_164 = A_163 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1006,c_540]) ).

tff(c_1045,plain,
    ! [B_164,A_163] :
      ( ( relation_image('#skF_16',set_intersection2(singleton(B_164),singleton(A_163))) = '#skF_9' )
      | ( B_164 = A_163 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_354,c_1018]) ).

tff(c_22785,plain,
    ! [B_50] : ( set_intersection2(relation_image('#skF_16',B_50),singleton(apply('#skF_16','#skF_3'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_50,singleton('#skF_3'('#skF_16')))) ),
    inference(negUnitSimplification,[status(thm)],[c_124,c_22784]) ).

tff(c_36,plain,
    ! [A_15] :
      ( ( apply(A_15,'#skF_4'(A_15)) = apply(A_15,'#skF_3'(A_15)) )
      | one_to_one(A_15)
      | ~ function(A_15)
      | ~ relation(A_15) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_38,plain,
    ! [A_15] :
      ( in('#skF_4'(A_15),relation_dom(A_15))
      | one_to_one(A_15)
      | ~ function(A_15)
      | ~ relation(A_15) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_24266,plain,
    ! [A_5908] :
      ( ( relation_image(A_5908,singleton('#skF_4'(A_5908))) = singleton(apply(A_5908,'#skF_4'(A_5908))) )
      | one_to_one(A_5908)
      | ~ function(A_5908)
      | ~ relation(A_5908) ),
    inference(resolution,[status(thm)],[c_38,c_5394]) ).

tff(c_24309,plain,
    ! [B_50] :
      ( ( set_intersection2(relation_image('#skF_16',B_50),singleton(apply('#skF_16','#skF_4'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_50,singleton('#skF_4'('#skF_16')))) )
      | one_to_one('#skF_16')
      | ~ function('#skF_16')
      | ~ relation('#skF_16') ),
    inference(superposition,[status(thm),theory(equality)],[c_24266,c_126]) ).

tff(c_24444,plain,
    ! [B_50] :
      ( ( set_intersection2(relation_image('#skF_16',B_50),singleton(apply('#skF_16','#skF_4'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_50,singleton('#skF_4'('#skF_16')))) )
      | one_to_one('#skF_16') ),
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_128,c_24309]) ).

tff(c_35513,plain,
    ! [B_12732] : ( set_intersection2(relation_image('#skF_16',B_12732),singleton(apply('#skF_16','#skF_4'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_12732,singleton('#skF_4'('#skF_16')))) ),
    inference(negUnitSimplification,[status(thm)],[c_124,c_24444]) ).

tff(c_35648,plain,
    ! [B_12732] :
      ( ( set_intersection2(relation_image('#skF_16',B_12732),singleton(apply('#skF_16','#skF_3'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_12732,singleton('#skF_4'('#skF_16')))) )
      | one_to_one('#skF_16')
      | ~ function('#skF_16')
      | ~ relation('#skF_16') ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_35513]) ).

tff(c_35829,plain,
    ! [B_12732] :
      ( ( relation_image('#skF_16',set_intersection2(B_12732,singleton('#skF_4'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_12732,singleton('#skF_3'('#skF_16')))) )
      | one_to_one('#skF_16') ),
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_128,c_22785,c_35648]) ).

tff(c_36894,plain,
    ! [B_12919] : ( relation_image('#skF_16',set_intersection2(B_12919,singleton('#skF_4'('#skF_16')))) = relation_image('#skF_16',set_intersection2(B_12919,singleton('#skF_3'('#skF_16')))) ),
    inference(negUnitSimplification,[status(thm)],[c_124,c_35829]) ).

tff(c_99962,plain,
    ! [B_17709] :
      ( ( relation_image('#skF_16',set_intersection2(singleton(B_17709),singleton('#skF_3'('#skF_16')))) = '#skF_9' )
      | ( B_17709 = '#skF_4'('#skF_16') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1045,c_36894]) ).

tff(c_100258,plain,
    ( ( relation_image('#skF_16',singleton('#skF_3'('#skF_16'))) = '#skF_9' )
    | ( '#skF_4'('#skF_16') = '#skF_3'('#skF_16') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_68,c_99962]) ).

tff(c_100325,plain,
    ( ( singleton(apply('#skF_16','#skF_3'('#skF_16'))) = '#skF_9' )
    | ( '#skF_4'('#skF_16') = '#skF_3'('#skF_16') ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_23440,c_100258]) ).

tff(c_100327,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1341,c_1137,c_100325]) ).

tff(c_100328,plain,
    ! [B_33] : empty(B_33),
    inference(splitRight,[status(thm)],[c_70]) ).

tff(c_52,plain,
    ! [A_26] : ~ empty(powerset(A_26)),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_100362,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_100328,c_52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU053+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.35  % Computer : n025.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 11:50:49 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 28.54/15.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.54/15.43  
% 28.54/15.43  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.68/15.46  
% 28.68/15.46  Inference rules
% 28.68/15.46  ----------------------
% 28.68/15.46  #Ref     : 16
% 28.68/15.46  #Sup     : 27617
% 28.68/15.46  #Fact    : 0
% 28.68/15.46  #Define  : 0
% 28.68/15.46  #Split   : 33
% 28.68/15.46  #Chain   : 0
% 28.68/15.46  #Close   : 0
% 28.68/15.46  
% 28.68/15.46  Ordering : KBO
% 28.68/15.46  
% 28.68/15.46  Simplification rules
% 28.68/15.46  ----------------------
% 28.68/15.46  #Subsume      : 15465
% 28.68/15.46  #Demod        : 7392
% 28.68/15.46  #Tautology    : 2592
% 28.68/15.46  #SimpNegUnit  : 890
% 28.68/15.46  #BackRed      : 481
% 28.68/15.46  
% 28.68/15.46  #Partial instantiations: 21597
% 28.68/15.46  #Strategies tried      : 1
% 28.68/15.46  
% 28.68/15.46  Timing (in seconds)
% 28.68/15.46  ----------------------
% 28.68/15.47  Preprocessing        : 0.62
% 28.68/15.47  Parsing              : 0.31
% 28.68/15.47  CNF conversion       : 0.05
% 28.68/15.47  Main loop            : 13.76
% 28.68/15.47  Inferencing          : 1.94
% 28.68/15.47  Reduction            : 6.35
% 28.68/15.47  Demodulation         : 5.25
% 28.68/15.47  BG Simplification    : 0.21
% 28.68/15.47  Subsumption          : 4.46
% 28.68/15.47  Abstraction          : 0.30
% 28.68/15.47  MUC search           : 0.00
% 28.68/15.47  Cooper               : 0.00
% 28.68/15.47  Total                : 14.45
% 28.68/15.47  Index Insertion      : 0.00
% 28.68/15.47  Index Deletion       : 0.00
% 28.68/15.47  Index Matching       : 0.00
% 28.68/15.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------