TSTP Solution File: DAT048_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT048_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n013.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 10:37:02 EDT 2023

% Result   : Theorem 22.68s 9.22s
% Output   : CNFRefutation 23.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  190 (  61 unt;  12 typ;   0 def)
%            Number of atoms       :  333 ( 270 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  295 ( 140   ~; 146   |;   1   &)
%                                         (   7 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number arithmetic     :  531 (   0 atm;  67 fun; 317 num; 147 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  10 usr;  12 con; 0-2 aty)
%            Number of variables   :  247 (; 247   !;   0   ?; 247   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty

%Foreground sorts:
tff(collection,type,
    collection: $tType ).

%Background operators:
tff('#skE_2',type,
    '#skE_2': $int ).

tff('#skE_1',type,
    '#skE_1': $int ).

tff('#skE_6',type,
    '#skE_6': $int ).

tff('#skE_5',type,
    '#skE_5': $int ).

tff('#skE_4',type,
    '#skE_4': $int ).

tff('#skE_3',type,
    '#skE_3': $int ).

%Foreground operators:
tff(empty,type,
    empty: collection ).

tff(count,type,
    count: collection > $int ).

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

tff(remove,type,
    remove: ( $int * collection ) > collection ).

tff(add,type,
    add: ( $int * collection ) > collection ).

tff(f_71,axiom,
    ! [Za: $int,X1: collection,X2a: $int] :
      ( ( in(Za,X1)
        | ( Za = X2a ) )
    <=> in(Za,add(X2a,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4) ).

tff(f_78,axiom,
    ! [X3a: $int,X4: collection,X5a: $int] :
      ( ( in(X3a,X4)
        & ( X3a != X5a ) )
    <=> in(X3a,remove(X5a,X4)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax5) ).

tff(f_139,negated_conjecture,
    count(add(1,add(5,remove(3,add(2,empty))))) != 3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_126,axiom,
    ! [X12a: $int,X13: collection] :
      ( in(X12a,X13)
    <=> ( count(remove(X12a,X13)) = $difference(count(X13),1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5) ).

tff(f_60,axiom,
    ! [Ua: $int] : ~ in(Ua,empty),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1) ).

tff(f_131,axiom,
    ! [X14a: $int,X15: collection] :
      ( ~ in(X14a,X15)
    <=> ( count(remove(X14a,X15)) = count(X15) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax6) ).

tff(f_113,axiom,
    ! [X7: collection] :
      ( ( X7 = empty )
    <=> ( count(X7) = 0 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2) ).

tff(f_118,axiom,
    ! [X8a: $int,X9: collection] :
      ( ~ in(X8a,X9)
    <=> ( count(add(X8a,X9)) = $sum(count(X9),1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3) ).

tff(f_122,axiom,
    ! [X10a: $int,X11: collection] :
      ( in(X10a,X11)
    <=> ( count(add(X10a,X11)) = count(X11) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4) ).

tff(f_135,axiom,
    ! [X16a: $int,X17: collection] :
      ( in(X16a,X17)
     => ( X17 = add(X16a,remove(X16a,X17)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7) ).

tff(c_65,plain,
    ! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_63,plain,
    ! [X3_9a: $int,X5_11a: $int,X4_10: collection] :
      ( in(X3_9a,remove(X5_11a,X4_10))
      | ~ in(X3_9a,X4_10)
      | ( X5_11a = X3_9a ) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_48,plain,
    count(add(1,add(5,remove(3,add(2,empty))))) != 3,
    inference(cnfTransformation,[status(thm)],[f_139]) ).

tff(c_117,plain,
    count(add(1,add(5,remove(3,add(2,empty))))) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_48]) ).

tff(c_35,plain,
    ! [X12_18a: $int,X13_19: collection] :
      ( ( count(remove(X12_18a,X13_19)) = $difference(count(X13_19),1) )
      | ~ in(X12_18a,X13_19) ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_610,plain,
    ! [X12_77a: $int,X13_78: collection] :
      ( ( count(remove(X12_77a,X13_78)) = $sum($uminus(1),count(X13_78)) )
      | ~ in(X12_77a,X13_78) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).

tff(c_1750,plain,
    ! [X2_134a: $int,X1_135: collection] : ( count(remove(X2_134a,add(X2_134a,X1_135))) = $sum($uminus(1),count(add(X2_134a,X1_135))) ),
    inference(resolution,[status(thm)],[c_65,c_610]) ).

tff(c_64,plain,
    ! [Z_6a: $int,X1_7: collection,X2_8a: $int] :
      ( ~ in(Z_6a,X1_7)
      | in(Z_6a,add(X2_8a,X1_7)) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_69,plain,
    ! [U_1a: $int] : ~ in(U_1a,empty),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_120,plain,
    ! [X14_40a: $int,X15_41: collection] :
      ( ( count(remove(X14_40a,X15_41)) = count(X15_41) )
      | in(X14_40a,X15_41) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_62,plain,
    ! [X3_9a: $int,X4_10: collection] : ~ in(X3_9a,remove(X3_9a,X4_10)),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_391,plain,
    ! [X14_65a: $int,X4_66: collection] : ( count(remove(X14_65a,remove(X14_65a,X4_66))) = count(remove(X14_65a,X4_66)) ),
    inference(resolution,[status(thm)],[c_120,c_62]) ).

tff(c_58,plain,
    ! [X7_13: collection] :
      ( ( empty = X7_13 )
      | ( count(X7_13) != 0 ) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_485,plain,
    ! [X14_71a: $int,X4_72: collection] :
      ( ( remove(X14_71a,remove(X14_71a,X4_72)) = empty )
      | ( count(remove(X14_71a,X4_72)) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_391,c_58]) ).

tff(c_503,plain,
    ! [X3_9a: $int,X14_71a: $int,X4_72: collection] :
      ( in(X3_9a,empty)
      | ~ in(X3_9a,remove(X14_71a,X4_72))
      | ( X3_9a = X14_71a )
      | ( count(remove(X14_71a,X4_72)) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_485,c_63]) ).

tff(c_998,plain,
    ! [X3_95a: $int,X14_96a: $int,X4_97: collection] :
      ( ~ in(X3_95a,remove(X14_96a,X4_97))
      | ( X3_95a = X14_96a )
      | ( count(remove(X14_96a,X4_97)) != 0 ) ),
    inference(negUnitSimplification,[status(thm)],[c_69,c_503]) ).

tff(c_1097,plain,
    ! [X5_100a: $int,X4_101: collection,X3_102a: $int] :
      ( ( count(remove(X5_100a,X4_101)) != 0 )
      | ~ in(X3_102a,X4_101)
      | ( X5_100a = X3_102a ) ),
    inference(resolution,[status(thm)],[c_63,c_998]) ).

tff(c_1508,plain,
    ! [X5_119a: $int,X2_120a: $int,X1_121: collection,Z_122a: $int] :
      ( ( count(remove(X5_119a,add(X2_120a,X1_121))) != 0 )
      | ( Z_122a = X5_119a )
      | ~ in(Z_122a,X1_121) ),
    inference(resolution,[status(thm)],[c_64,c_1097]) ).

tff(c_1548,plain,
    ! [X5_119a: $int,X2_120a: $int,X2_8a: $int,X1_7: collection] :
      ( ( count(remove(X5_119a,add(X2_120a,add(X2_8a,X1_7)))) != 0 )
      | ( X5_119a = X2_8a ) ),
    inference(resolution,[status(thm)],[c_65,c_1508]) ).

tff(c_1763,plain,
    ! [X2_134a: $int,X2_8a: $int,X1_7: collection] :
      ( ( $sum($uminus(1),count(add(X2_134a,add(X2_8a,X1_7)))) != 0 )
      | ( X2_8a = X2_134a ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1750,c_1548]) ).

tff(c_1965,plain,
    ! [X2_144a: $int,X2_145a: $int,X1_146: collection] :
      ( ( count(add(X2_144a,add(X2_145a,X1_146))) != 1 )
      | ( X2_145a = X2_144a ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1763]) ).

tff(c_1983,plain,
    ( ( '#skE_1' != 1 )
    | ( 5 = 1 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_117,c_1965]) ).

tff(c_1991,plain,
    '#skE_1' != 1,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1983]) ).

tff(c_59,plain,
    count(empty) = 0,
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_25,plain,
    ! [X8_14a: $int,X9_15: collection] :
      ( ( count(add(X8_14a,X9_15)) = $sum(count(X9_15),1) )
      | in(X8_14a,X9_15) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_330,plain,
    ! [X8_62a: $int,X9_63: collection] :
      ( ( count(add(X8_62a,X9_63)) = $sum(1,count(X9_63)) )
      | in(X8_62a,X9_63) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).

tff(c_355,plain,
    ! [X8_62a: $int] : ( count(add(X8_62a,empty)) = $sum(1,count(empty)) ),
    inference(resolution,[status(thm)],[c_330,c_69]) ).

tff(c_369,plain,
    ! [X8_62a: $int] : ( count(add(X8_62a,empty)) = $sum(1,0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_59,c_355]) ).

tff(c_371,plain,
    ! [X8_62a: $int] : ( count(add(X8_62a,empty)) = 1 ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_369]) ).

tff(c_51,plain,
    ! [X14_20a: $int,X15_21: collection] :
      ( ( count(remove(X14_20a,X15_21)) = count(X15_21) )
      | in(X14_20a,X15_21) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_196,plain,
    ! [X10_46a: $int,X11_47: collection] :
      ( ( count(add(X10_46a,X11_47)) = count(X11_47) )
      | ~ in(X10_46a,X11_47) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_210,plain,
    ! [X14_20a: $int,X15_21: collection] :
      ( ( count(add(X14_20a,X15_21)) = count(X15_21) )
      | ( count(remove(X14_20a,X15_21)) = count(X15_21) ) ),
    inference(resolution,[status(thm)],[c_51,c_196]) ).

tff(c_132,plain,
    ! [X14_40a: $int] : ( count(remove(X14_40a,empty)) = count(empty) ),
    inference(resolution,[status(thm)],[c_120,c_69]) ).

tff(c_140,plain,
    ! [X14_42a: $int] : ( count(remove(X14_42a,empty)) = 0 ),
    inference(demodulation,[status(thm),theory(equality)],[c_59,c_132]) ).

tff(c_153,plain,
    ! [X14_42a: $int] : ( remove(X14_42a,empty) = empty ),
    inference(superposition,[status(thm),theory(equality)],[c_140,c_58]) ).

tff(c_709,plain,
    ! [X8_83a: $int,X4_84: collection] : ( count(add(X8_83a,remove(X8_83a,X4_84))) = $sum(1,count(remove(X8_83a,X4_84))) ),
    inference(resolution,[status(thm)],[c_330,c_62]) ).

tff(c_717,plain,
    ! [X8_83a: $int,X4_84: collection] :
      ( ( add(X8_83a,remove(X8_83a,X4_84)) = empty )
      | ( $sum(1,count(remove(X8_83a,X4_84))) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_709,c_58]) ).

tff(c_1613,plain,
    ! [X8_129a: $int,X4_130: collection] :
      ( ( add(X8_129a,remove(X8_129a,X4_130)) = empty )
      | ( count(remove(X8_129a,X4_130)) != $uminus(1) ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_717]) ).

tff(c_1132,plain,
    ! [X5_100a: $int,X2_8a: $int,X1_7: collection] :
      ( ( count(remove(X5_100a,add(X2_8a,X1_7))) != 0 )
      | ( X5_100a = X2_8a ) ),
    inference(resolution,[status(thm)],[c_65,c_1097]) ).

tff(c_1622,plain,
    ! [X5_100a: $int,X8_129a: $int,X4_130: collection] :
      ( ( count(remove(X5_100a,empty)) != 0 )
      | ( X8_129a = X5_100a )
      | ( count(remove(X8_129a,X4_130)) != $uminus(1) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1613,c_1132]) ).

tff(c_1715,plain,
    ! [X8_131a: $int,X5_132a: $int,X4_133: collection] :
      ( ( X8_131a = X5_132a )
      | ( count(remove(X8_131a,X4_133)) != $uminus(1) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_59,c_153,c_1622]) ).

tff(c_3557,plain,
    ! [X5_200a: $int,X14_201a: $int,X15_202: collection] :
      ( ( X5_200a = X14_201a )
      | ( count(X15_202) != $uminus(1) )
      | ( count(add(X14_201a,X15_202)) = count(X15_202) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_210,c_1715]) ).

tff(c_3669,plain,
    ! [X5_200a: $int] :
      ( ( X5_200a = 1 )
      | ( count(add(5,remove(3,add(2,empty)))) != $uminus(1) )
      | ( count(add(5,remove(3,add(2,empty)))) = '#skE_1' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_117,c_3557]) ).

tff(c_3899,plain,
    count(add(5,remove(3,add(2,empty)))) = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_3669]) ).

tff(c_54,plain,
    ! [X10_16a: $int,X11_17: collection] :
      ( in(X10_16a,X11_17)
      | ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_175,plain,
    ! [X16_44a: $int,X17_45: collection] :
      ( ( add(X16_44a,remove(X16_44a,X17_45)) = X17_45 )
      | ~ in(X16_44a,X17_45) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_750,plain,
    ! [X10_85a: $int,X11_86: collection] :
      ( ( add(X10_85a,remove(X10_85a,X11_86)) = X11_86 )
      | ( count(add(X10_85a,X11_86)) != count(X11_86) ) ),
    inference(resolution,[status(thm)],[c_54,c_175]) ).

tff(c_308,plain,
    ! [X2_58a: $int,X1_59: collection] : ( count(add(X2_58a,add(X2_58a,X1_59))) = count(add(X2_58a,X1_59)) ),
    inference(resolution,[status(thm)],[c_65,c_196]) ).

tff(c_552,plain,
    ! [X2_75a: $int,X1_76: collection] :
      ( ( add(X2_75a,add(X2_75a,X1_76)) = empty )
      | ( count(add(X2_75a,X1_76)) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_308,c_58]) ).

tff(c_579,plain,
    ! [X2_75a: $int,X1_76: collection] :
      ( in(X2_75a,empty)
      | ( count(add(X2_75a,X1_76)) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_552,c_65]) ).

tff(c_604,plain,
    ! [X2_75a: $int,X1_76: collection] : ( count(add(X2_75a,X1_76)) != 0 ),
    inference(negUnitSimplification,[status(thm)],[c_69,c_579]) ).

tff(c_797,plain,
    ! [X11_86: collection,X10_85a: $int] :
      ( ( count(X11_86) != 0 )
      | ( count(add(X10_85a,X11_86)) != count(X11_86) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_750,c_604]) ).

tff(c_4041,plain,
    ( ( count(remove(3,add(2,empty))) != 0 )
    | ( count(remove(3,add(2,empty))) != '#skE_2' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3899,c_797]) ).

tff(c_4629,plain,
    count(remove(3,add(2,empty))) = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_4041]) ).

tff(c_4705,plain,
    ( ( count(add(2,empty)) = '#skE_3' )
    | ( count(add(3,add(2,empty))) = count(add(2,empty)) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_210,c_4629]) ).

tff(c_4763,plain,
    ( ( '#skE_3' = 1 )
    | ( count(add(3,add(2,empty))) = 1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_371,c_371,c_4705]) ).

tff(c_4768,plain,
    count(add(3,add(2,empty))) = '#skE_4',
    inference(define,[status(thm),theory(equality)],[c_4763]) ).

tff(c_4772,plain,
    ( ( '#skE_3' = 1 )
    | ( '#skE_4' = 1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4768,c_4763]) ).

tff(c_4774,plain,
    '#skE_4' = 1,
    inference(splitLeft,[status(thm)],[c_4772]) ).

tff(c_4771,plain,
    count(add(3,add(2,empty))) = '#skE_4',
    inference(define,[status(thm),theory(equality)],[c_4763]) ).

tff(c_4776,plain,
    count(add(3,add(2,empty))) = 1,
    inference(demodulation,[status(thm),theory(equality)],[c_4774,c_4771]) ).

tff(c_1826,plain,
    ! [X2_134a: $int,X2_8a: $int,X1_7: collection] :
      ( ( count(add(X2_134a,add(X2_8a,X1_7))) != 1 )
      | ( X2_8a = X2_134a ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1763]) ).

tff(c_4868,plain,
    3 = 2,
    inference(superposition,[status(thm),theory(equality)],[c_4776,c_1826]) ).

tff(c_4871,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4868]) ).

tff(c_4874,plain,
    '#skE_3' = 1,
    inference(splitRight,[status(thm)],[c_4772]) ).

tff(c_1742,plain,
    ! [X5_132a: $int,X14_20a: $int,X15_21: collection] :
      ( ( X5_132a = X14_20a )
      | ( count(X15_21) != $uminus(1) )
      | ( count(add(X14_20a,X15_21)) = count(X15_21) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_210,c_1715]) ).

tff(c_4030,plain,
    ! [X5_132a: $int] :
      ( ( X5_132a = 5 )
      | ( count(remove(3,add(2,empty))) != $uminus(1) )
      | ( count(remove(3,add(2,empty))) = '#skE_2' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3899,c_1742]) ).

tff(c_4985,plain,
    count(remove(3,add(2,empty))) = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_4030]) ).

tff(c_4989,plain,
    count(remove(3,add(2,empty))) = 1,
    inference(demodulation,[status(thm),theory(equality)],[c_4874,c_4985]) ).

tff(c_28,plain,
    ! [X8_14a: $int,X9_15: collection] :
      ( ~ in(X8_14a,X9_15)
      | ( count(add(X8_14a,X9_15)) != $sum(count(X9_15),1) ) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_452,plain,
    ! [X8_69a: $int,X9_70: collection] :
      ( ~ in(X8_69a,X9_70)
      | ( count(add(X8_69a,X9_70)) != $sum(1,count(X9_70)) ) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).

tff(c_5280,plain,
    ! [X10_215a: $int,X11_216: collection] :
      ( ( count(add(X10_215a,X11_216)) != $sum(1,count(X11_216)) )
      | ( count(add(X10_215a,X11_216)) != count(X11_216) ) ),
    inference(resolution,[status(thm)],[c_54,c_452]) ).

tff(c_5322,plain,
    ( ( $sum(1,count(add(5,remove(3,add(2,empty))))) != '#skE_1' )
    | ( count(add(1,add(5,remove(3,add(2,empty))))) != count(add(5,remove(3,add(2,empty)))) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_117,c_5280]) ).

tff(c_5358,plain,
    ( ( $sum(1,'#skE_2') != '#skE_1' )
    | ( '#skE_2' != '#skE_1' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_117,c_3899,c_3899,c_5322]) ).

tff(c_5360,plain,
    ( ( '#skE_2' != $sum($uminus(1),'#skE_1') )
    | ( '#skE_2' != '#skE_1' ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5358]) ).

tff(c_5362,plain,
    '#skE_2' != '#skE_1',
    inference(splitLeft,[status(thm)],[c_5360]) ).

tff(c_55,plain,
    ! [X10_16a: $int,X11_17: collection] :
      ( ( count(add(X10_16a,X11_17)) = count(X11_17) )
      | ~ in(X10_16a,X11_17) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_3678,plain,
    ! [X8_203a: $int,X9_204: collection] :
      ( ( count(add(X8_203a,X9_204)) = count(X9_204) )
      | ( count(add(X8_203a,X9_204)) = $sum(1,count(X9_204)) ) ),
    inference(resolution,[status(thm)],[c_330,c_55]) ).

tff(c_3729,plain,
    ( ( $sum(1,count(add(5,remove(3,add(2,empty))))) = '#skE_1' )
    | ( count(add(1,add(5,remove(3,add(2,empty))))) = count(add(5,remove(3,add(2,empty)))) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3678,c_117]) ).

tff(c_3796,plain,
    ( ( $sum(1,count(add(5,remove(3,add(2,empty))))) = '#skE_1' )
    | ( count(add(5,remove(3,add(2,empty)))) = '#skE_1' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_117,c_3729]) ).

tff(c_3798,plain,
    ( ( count(add(5,remove(3,add(2,empty)))) = $sum($uminus(1),'#skE_1') )
    | ( count(add(5,remove(3,add(2,empty)))) = '#skE_1' ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3796]) ).

tff(c_5365,plain,
    ( ( '#skE_2' = $sum($uminus(1),'#skE_1') )
    | ( '#skE_2' = '#skE_1' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3899,c_3899,c_3798]) ).

tff(c_5367,plain,
    '#skE_2' = $sum($uminus(1),'#skE_1'),
    inference(negUnitSimplification,[status(thm)],[c_5362,c_5365]) ).

tff(c_640,plain,
    ! [X2_8a: $int,X1_7: collection] : ( count(remove(X2_8a,add(X2_8a,X1_7))) = $sum($uminus(1),count(add(X2_8a,X1_7))) ),
    inference(resolution,[status(thm)],[c_65,c_610]) ).

tff(c_919,plain,
    ! [X14_93a: $int,X15_94: collection] :
      ( ( add(X14_93a,remove(X14_93a,X15_94)) = X15_94 )
      | ( count(remove(X14_93a,X15_94)) = count(X15_94) ) ),
    inference(resolution,[status(thm)],[c_51,c_175]) ).

tff(c_1036,plain,
    ! [X15_98: collection,X14_99a: $int] :
      ( ( count(X15_98) != 0 )
      | ( count(remove(X14_99a,X15_98)) = count(X15_98) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_919,c_604]) ).

tff(c_1086,plain,
    ! [X14_99a: $int,X15_98: collection] :
      ( ( remove(X14_99a,X15_98) = empty )
      | ( count(X15_98) != 0 )
      | ( count(X15_98) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1036,c_58]) ).

tff(c_136,plain,
    ! [X14_40a: $int,X4_10: collection] : ( count(remove(X14_40a,remove(X14_40a,X4_10))) = count(remove(X14_40a,X4_10)) ),
    inference(resolution,[status(thm)],[c_120,c_62]) ).

tff(c_94,plain,
    ! [X10_37a: $int,X11_38: collection] :
      ( in(X10_37a,X11_38)
      | ( count(add(X10_37a,X11_38)) != count(X11_38) ) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_110,plain,
    ! [X10_37a: $int,X4_10: collection] : ( count(add(X10_37a,remove(X10_37a,X4_10))) != count(remove(X10_37a,X4_10)) ),
    inference(resolution,[status(thm)],[c_94,c_62]) ).

tff(c_500,plain,
    ! [X14_71a: $int,X4_72: collection] :
      ( ( count(remove(X14_71a,remove(X14_71a,X4_72))) != count(add(X14_71a,empty)) )
      | ( count(remove(X14_71a,X4_72)) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_485,c_110]) ).

tff(c_528,plain,
    ! [X14_71a: $int,X4_72: collection] :
      ( ( count(remove(X14_71a,X4_72)) != 1 )
      | ( count(remove(X14_71a,X4_72)) != 0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_136,c_371,c_500]) ).

tff(c_1269,plain,
    ! [X15_108: collection,X14_109a: $int] :
      ( ( count(X15_108) != 1 )
      | ( count(remove(X14_109a,X15_108)) != 0 )
      | ( count(X15_108) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1036,c_528]) ).

tff(c_1272,plain,
    ! [X15_98: collection] :
      ( ( count(X15_98) != 1 )
      | ( count(empty) != 0 )
      | ( count(X15_98) != 0 )
      | ( count(X15_98) != 0 )
      | ( count(X15_98) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1086,c_1269]) ).

tff(c_1290,plain,
    ! [X15_98: collection] :
      ( ( count(X15_98) != 1 )
      | ( count(X15_98) != 0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_59,c_1272]) ).

tff(c_1769,plain,
    ! [X2_134a: $int,X1_135: collection] :
      ( ( $sum($uminus(1),count(add(X2_134a,X1_135))) != 1 )
      | ( count(remove(X2_134a,add(X2_134a,X1_135))) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1750,c_1290]) ).

tff(c_1827,plain,
    ! [X2_134a: $int,X1_135: collection] :
      ( ( $sum($uminus(1),count(add(X2_134a,X1_135))) != 1 )
      | ( $sum($uminus(1),count(add(X2_134a,X1_135))) != 0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_640,c_1769]) ).

tff(c_1829,plain,
    ! [X2_134a: $int,X1_135: collection] :
      ( ( count(add(X2_134a,X1_135)) != 2 )
      | ( count(add(X2_134a,X1_135)) != 1 ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1827]) ).

tff(c_3990,plain,
    ( ( '#skE_2' != 2 )
    | ( count(add(5,remove(3,add(2,empty)))) != 1 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3899,c_1829]) ).

tff(c_4035,plain,
    ( ( '#skE_2' != 2 )
    | ( '#skE_2' != 1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3899,c_3990]) ).

tff(c_4064,plain,
    '#skE_2' != 1,
    inference(splitLeft,[status(thm)],[c_4035]) ).

tff(c_5371,plain,
    $sum($uminus(1),'#skE_1') != 1,
    inference(demodulation,[status(thm),theory(equality)],[c_5367,c_4064]) ).

tff(c_5379,plain,
    '#skE_1' != 2,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5371]) ).

tff(c_114,plain,
    count(add(1,add(5,remove(3,add(2,empty))))) = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_48]) ).

tff(c_118,plain,
    '#skE_1' != 3,
    inference(demodulation,[status(thm),theory(equality)],[c_114,c_48]) ).

tff(c_5381,plain,
    count(add(5,remove(3,add(2,empty)))) = $sum($uminus(1),'#skE_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_5367,c_3899]) ).

tff(c_361,plain,
    ! [X8_62a: $int,X9_63: collection] :
      ( ( count(add(X8_62a,X9_63)) = count(X9_63) )
      | ( count(add(X8_62a,X9_63)) = $sum(1,count(X9_63)) ) ),
    inference(resolution,[status(thm)],[c_330,c_55]) ).

tff(c_5901,plain,
    ( ( $sum(1,count(remove(3,add(2,empty)))) = $sum($uminus(1),'#skE_1') )
    | ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_361,c_5381]) ).

tff(c_5973,plain,
    ( ( $sum($uminus(1),'#skE_1') = $sum(1,1) )
    | ( $sum($uminus(1),'#skE_1') = 1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_5381,c_4989,c_4989,c_5901]) ).

tff(c_5975,plain,
    ( ( '#skE_1' = 3 )
    | ( '#skE_1' = 2 ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5973]) ).

tff(c_5988,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5379,c_118,c_5975]) ).

tff(c_5992,plain,
    '#skE_2' = '#skE_1',
    inference(splitRight,[status(thm)],[c_5360]) ).

tff(c_5999,plain,
    count(add(5,remove(3,add(2,empty)))) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_5992,c_3899]) ).

tff(c_6099,plain,
    ( ( count(add(5,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
    | ( $sum(1,count(remove(3,add(2,empty)))) = '#skE_1' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5999,c_361]) ).

tff(c_6156,plain,
    ( ( '#skE_1' = 1 )
    | ( '#skE_1' = $sum(1,1) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4989,c_5999,c_4989,c_6099]) ).

tff(c_6157,plain,
    '#skE_1' = $sum(1,1),
    inference(negUnitSimplification,[status(thm)],[c_1991,c_6156]) ).

tff(c_6159,plain,
    '#skE_1' = 2,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6157]) ).

tff(c_6200,plain,
    count(add(5,remove(3,add(2,empty)))) = 2,
    inference(demodulation,[status(thm),theory(equality)],[c_6159,c_5999]) ).

tff(c_6202,plain,
    count(add(1,add(5,remove(3,add(2,empty))))) = 2,
    inference(demodulation,[status(thm),theory(equality)],[c_6159,c_117]) ).

tff(c_283,plain,
    ! [Z_53a: $int,X1_54: collection,X2_55a: $int] :
      ( in(Z_53a,X1_54)
      | ~ in(Z_53a,add(X2_55a,X1_54))
      | ( Z_53a = X2_55a ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_11020,plain,
    ! [X10_293a: $int,X1_294: collection,X2_295a: $int] :
      ( in(X10_293a,X1_294)
      | ( X2_295a = X10_293a )
      | ( count(add(X10_293a,add(X2_295a,X1_294))) != count(add(X2_295a,X1_294)) ) ),
    inference(resolution,[status(thm)],[c_54,c_283]) ).

tff(c_70908,plain,
    ! [X10_888a: $int,X1_889: collection,X2_890a: $int] :
      ( ( count(add(X10_888a,X1_889)) = count(X1_889) )
      | ( X2_890a = X10_888a )
      | ( count(add(X10_888a,add(X2_890a,X1_889))) != count(add(X2_890a,X1_889)) ) ),
    inference(resolution,[status(thm)],[c_11020,c_55]) ).

tff(c_71076,plain,
    ( ( count(add(1,remove(3,add(2,empty)))) = count(remove(3,add(2,empty))) )
    | ( 5 = 1 )
    | ( count(add(5,remove(3,add(2,empty)))) != 2 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_6202,c_70908]) ).

tff(c_71194,plain,
    ( ( count(add(1,remove(3,add(2,empty)))) = 1 )
    | ( 5 = 1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6200,c_4989,c_71076]) ).

tff(c_71196,plain,
    count(add(1,remove(3,add(2,empty)))) = 1,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_71194]) ).

tff(c_238,plain,
    ! [X3_50a: $int,X5_51a: $int,X4_52: collection] :
      ( in(X3_50a,remove(X5_51a,X4_52))
      | ~ in(X3_50a,X4_52)
      | ( X5_51a = X3_50a ) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_49,plain,
    ! [X16_22a: $int,X17_23: collection] :
      ( ( add(X16_22a,remove(X16_22a,X17_23)) = X17_23 )
      | ~ in(X16_22a,X17_23) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_10739,plain,
    ! [X3_288a: $int,X5_289a: $int,X4_290: collection] :
      ( ( add(X3_288a,remove(X3_288a,remove(X5_289a,X4_290))) = remove(X5_289a,X4_290) )
      | ~ in(X3_288a,X4_290)
      | ( X5_289a = X3_288a ) ),
    inference(resolution,[status(thm)],[c_238,c_49]) ).

tff(c_41714,plain,
    ! [X2_658a: $int,X5_659a: $int,X1_660: collection] :
      ( ( add(X2_658a,remove(X2_658a,remove(X5_659a,add(X2_658a,X1_660)))) = remove(X5_659a,add(X2_658a,X1_660)) )
      | ( X5_659a = X2_658a ) ),
    inference(resolution,[status(thm)],[c_65,c_10739]) ).

tff(c_3005,plain,
    ! [Z_189a: $int,X2_190a: $int,X1_191: collection] :
      ( ( add(Z_189a,remove(Z_189a,add(X2_190a,X1_191))) = add(X2_190a,X1_191) )
      | ~ in(Z_189a,X1_191) ),
    inference(resolution,[status(thm)],[c_64,c_175]) ).

tff(c_21129,plain,
    ! [X2_397a: $int,X2_398a: $int,X1_399: collection] : ( add(X2_397a,remove(X2_397a,add(X2_398a,add(X2_397a,X1_399)))) = add(X2_398a,add(X2_397a,X1_399)) ),
    inference(resolution,[status(thm)],[c_65,c_3005]) ).

tff(c_21583,plain,
    ! [X2_397a: $int,X2_398a: $int,X1_399: collection] : in(X2_397a,add(X2_398a,add(X2_397a,X1_399))),
    inference(superposition,[status(thm),theory(equality)],[c_21129,c_65]) ).

tff(c_42634,plain,
    ! [X2_664a: $int,X2_665a: $int,X5_666a: $int,X1_667: collection] :
      ( in(X2_664a,add(X2_665a,remove(X5_666a,add(X2_664a,X1_667))))
      | ( X5_666a = X2_664a ) ),
    inference(superposition,[status(thm),theory(equality)],[c_41714,c_21583]) ).

tff(c_1784,plain,
    ! [X2_134a: $int,X1_135: collection] :
      ( ( remove(X2_134a,add(X2_134a,X1_135)) = empty )
      | ( $sum($uminus(1),count(add(X2_134a,X1_135))) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1750,c_58]) ).

tff(c_2458,plain,
    ! [X2_161a: $int,X1_162: collection] :
      ( ( remove(X2_161a,add(X2_161a,X1_162)) = empty )
      | ( count(add(X2_161a,X1_162)) != 1 ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1784]) ).

tff(c_2528,plain,
    ! [X3_9a: $int,X2_161a: $int,X1_162: collection] :
      ( in(X3_9a,empty)
      | ~ in(X3_9a,add(X2_161a,X1_162))
      | ( X3_9a = X2_161a )
      | ( count(add(X2_161a,X1_162)) != 1 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2458,c_63]) ).

tff(c_2603,plain,
    ! [X3_9a: $int,X2_161a: $int,X1_162: collection] :
      ( ~ in(X3_9a,add(X2_161a,X1_162))
      | ( X3_9a = X2_161a )
      | ( count(add(X2_161a,X1_162)) != 1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_69,c_2528]) ).

tff(c_42851,plain,
    ! [X2_665a: $int,X2_664a: $int,X5_666a: $int,X1_667: collection] :
      ( ( X2_665a = X2_664a )
      | ( count(add(X2_665a,remove(X5_666a,add(X2_664a,X1_667)))) != 1 )
      | ( X5_666a = X2_664a ) ),
    inference(resolution,[status(thm)],[c_42634,c_2603]) ).

tff(c_71451,plain,
    ( ( 2 = 1 )
    | ( 3 = 2 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_71196,c_42851]) ).

tff(c_71454,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_71451]) ).

tff(c_71458,plain,
    '#skE_2' = 1,
    inference(splitRight,[status(thm)],[c_4035]) ).

tff(c_71465,plain,
    count(add(5,remove(3,add(2,empty)))) = 1,
    inference(demodulation,[status(thm),theory(equality)],[c_71458,c_3899]) ).

tff(c_195,plain,
    ! [X2_8a: $int,X1_7: collection] : ( add(X2_8a,remove(X2_8a,add(X2_8a,X1_7))) = add(X2_8a,X1_7) ),
    inference(resolution,[status(thm)],[c_65,c_175]) ).

tff(c_2598,plain,
    ! [X2_161a: $int,X1_162: collection] :
      ( ( add(X2_161a,empty) = add(X2_161a,X1_162) )
      | ( count(add(X2_161a,X1_162)) != 1 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2458,c_195]) ).

tff(c_71532,plain,
    add(5,remove(3,add(2,empty))) = add(5,empty),
    inference(superposition,[status(thm),theory(equality)],[c_71465,c_2598]) ).

tff(c_81905,plain,
    ! [Z_1020a: $int] :
      ( ~ in(Z_1020a,remove(3,add(2,empty)))
      | in(Z_1020a,add(5,empty)) ),
    inference(superposition,[status(thm),theory(equality)],[c_71532,c_64]) ).

tff(c_82958,plain,
    ! [X3_1041a: $int] :
      ( in(X3_1041a,add(5,empty))
      | ~ in(X3_1041a,add(2,empty))
      | ( X3_1041a = 3 ) ),
    inference(resolution,[status(thm)],[c_63,c_81905]) ).

tff(c_978,plain,
    ! [X15_94: collection,X14_93a: $int] :
      ( ( count(X15_94) != 0 )
      | ( count(remove(X14_93a,X15_94)) = count(X15_94) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_919,c_604]) ).

tff(c_50,plain,
    ! [X14_20a: $int,X15_21: collection] :
      ( ~ in(X14_20a,X15_21)
      | ( count(remove(X14_20a,X15_21)) != count(X15_21) ) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_72425,plain,
    ! [X8_896a: $int,X9_897: collection] :
      ( ( count(remove(X8_896a,X9_897)) != count(X9_897) )
      | ( count(add(X8_896a,X9_897)) = $sum(1,count(X9_897)) ) ),
    inference(resolution,[status(thm)],[c_330,c_50]) ).

tff(c_72500,plain,
    ! [X14_898a: $int,X15_899: collection] :
      ( ( count(add(X14_898a,X15_899)) = $sum(1,count(X15_899)) )
      | ( count(X15_899) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_978,c_72425]) ).

tff(c_72531,plain,
    ! [X14_898a: $int,X15_899: collection] :
      ( ( add(X14_898a,empty) = add(X14_898a,X15_899) )
      | ( $sum(1,count(X15_899)) != 1 )
      | ( count(X15_899) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_72500,c_2598]) ).

tff(c_74145,plain,
    ! [X14_912a: $int,X15_913: collection] :
      ( ( add(X14_912a,empty) = add(X14_912a,X15_913) )
      | ( count(X15_913) != 0 )
      | ( count(X15_913) != 0 ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_72531]) ).

tff(c_74250,plain,
    ! [X14_912a: $int,X15_913: collection] :
      ( ( add(X14_912a,empty) = add(X14_912a,X15_913) )
      | ( count(add(X14_912a,empty)) != 1 )
      | ( count(X15_913) != 0 )
      | ( count(X15_913) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_74145,c_2598]) ).

tff(c_75537,plain,
    ! [X14_930a: $int,X15_931: collection] :
      ( ( add(X14_930a,empty) = add(X14_930a,X15_931) )
      | ( count(X15_931) != 0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_371,c_74250]) ).

tff(c_1840,plain,
    ! [X2_134a: $int,X1_135: collection] :
      ( ( remove(X2_134a,add(X2_134a,X1_135)) = empty )
      | ( count(add(X2_134a,X1_135)) != 1 ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1784]) ).

tff(c_74270,plain,
    ! [X14_912a: $int,X15_913: collection] :
      ( ( remove(X14_912a,add(X14_912a,X15_913)) = empty )
      | ( count(add(X14_912a,empty)) != 1 )
      | ( count(X15_913) != 0 )
      | ( count(X15_913) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_74145,c_1840]) ).

tff(c_74486,plain,
    ! [X14_912a: $int,X15_913: collection] :
      ( ( remove(X14_912a,add(X14_912a,X15_913)) = empty )
      | ( count(X15_913) != 0 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_371,c_74270]) ).

tff(c_75844,plain,
    ! [X14_930a: $int,X15_931: collection] :
      ( ( remove(X14_930a,add(X14_930a,empty)) = empty )
      | ( count(X15_931) != 0 )
      | ( count(X15_931) != 0 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_75537,c_74486]) ).

tff(c_81102,plain,
    ! [X15_1010: collection] :
      ( ( count(X15_1010) != 0 )
      | ( count(X15_1010) != 0 ) ),
    inference(splitLeft,[status(thm)],[c_75844]) ).

tff(c_81158,plain,
    count(empty) != 0,
    inference(superposition,[status(thm),theory(equality)],[c_59,c_81102]) ).

tff(c_81203,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_59,c_81158]) ).

tff(c_81207,plain,
    ! [X14_1011a: $int] : ( remove(X14_1011a,add(X14_1011a,empty)) = empty ),
    inference(splitRight,[status(thm)],[c_75844]) ).

tff(c_81324,plain,
    ! [X3_9a: $int,X14_1011a: $int] :
      ( in(X3_9a,empty)
      | ~ in(X3_9a,add(X14_1011a,empty))
      | ( X3_9a = X14_1011a ) ),
    inference(superposition,[status(thm),theory(equality)],[c_81207,c_63]) ).

tff(c_81467,plain,
    ! [X3_9a: $int,X14_1011a: $int] :
      ( ~ in(X3_9a,add(X14_1011a,empty))
      | ( X3_9a = X14_1011a ) ),
    inference(negUnitSimplification,[status(thm)],[c_69,c_81324]) ).

tff(c_83113,plain,
    ! [X3_1042a: $int] :
      ( ( X3_1042a = 5 )
      | ~ in(X3_1042a,add(2,empty))
      | ( X3_1042a = 3 ) ),
    inference(resolution,[status(thm)],[c_82958,c_81467]) ).

tff(c_83211,plain,
    ( ( 5 = 2 )
    | ( 3 = 2 ) ),
    inference(resolution,[status(thm)],[c_65,c_83113]) ).

tff(c_83214,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_83211]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : DAT048_1 : TPTP v8.1.2. Released v5.0.0.
% 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
% 0.14/0.36  % Computer : n013.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 13:07:32 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 22.68/9.22  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.80/9.24  
% 22.80/9.24  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.04/9.29  
% 23.04/9.29  Inference rules
% 23.04/9.29  ----------------------
% 23.04/9.29  #Ref     : 0
% 23.04/9.29  #Sup     : 17750
% 23.04/9.29  #Fact    : 4
% 23.04/9.29  #Define  : 10
% 23.04/9.29  #Split   : 34
% 23.04/9.29  #Chain   : 0
% 23.04/9.29  #Close   : 0
% 23.04/9.29  
% 23.04/9.29  Ordering : LPO
% 23.04/9.29  
% 23.04/9.29  Simplification rules
% 23.04/9.29  ----------------------
% 23.04/9.29  #Subsume      : 5418
% 23.04/9.29  #Demod        : 8926
% 23.04/9.29  #Tautology    : 5883
% 23.04/9.29  #SimpNegUnit  : 146
% 23.04/9.29  #BackRed      : 21
% 23.04/9.29  
% 23.04/9.29  #Partial instantiations: 0
% 23.04/9.29  #Strategies tried      : 1
% 23.04/9.29  
% 23.04/9.29  Timing (in seconds)
% 23.04/9.29  ----------------------
% 23.42/9.37  Preprocessing        : 0.58
% 23.42/9.37  Parsing              : 0.31
% 23.42/9.37  CNF conversion       : 0.03
% 23.42/9.37  Main loop            : 7.62
% 23.42/9.37  Inferencing          : 1.47
% 23.42/9.37  Reduction            : 2.04
% 23.42/9.37  Demodulation         : 1.52
% 23.42/9.37  BG Simplification    : 0.50
% 23.42/9.37  Subsumption          : 3.01
% 23.42/9.37  Abstraction          : 0.27
% 23.42/9.37  MUC search           : 0.00
% 23.42/9.37  Cooper               : 0.03
% 23.42/9.37  Total                : 8.28
% 23.42/9.37  Index Insertion      : 0.00
% 23.42/9.37  Index Deletion       : 0.00
% 23.42/9.37  Index Matching       : 0.00
% 23.42/9.37  BG Taut test         : 0.00
%------------------------------------------------------------------------------