TSTP Solution File: SET598+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET598+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n007.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 10:56:39 EDT 2023

% Result   : Theorem 7.38s 2.98s
% Output   : CNFRefutation 7.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  110 (  44 unt;  13 typ;   0 def)
%            Number of atoms       :  206 (  31 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  214 ( 105   ~; 100   |;   5   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   44 (;  44   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > intersection > #nlpp > #skF_7 > #skF_3 > #skF_10 > #skF_5 > #skF_6 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_90,negated_conjecture,
    ~ ! [B,C,D] :
        ( ( B = intersection(C,D) )
      <=> ( subset(B,C)
          & subset(B,D)
          & ! [E] :
              ( ( subset(E,C)
                & subset(E,D) )
             => subset(E,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th57) ).

tff(f_32,axiom,
    ! [B,C] : subset(intersection(B,C),B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).

tff(f_64,axiom,
    ! [B,C] : ( intersection(B,C) = intersection(C,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

tff(f_39,axiom,
    ! [B,C,D] :
      ( ( subset(B,C)
        & subset(B,D) )
     => subset(B,intersection(C,D)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).

tff(f_61,axiom,
    ! [B,C] :
      ( ( B = C )
    <=> ( subset(B,C)
        & subset(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

tff(c_68,plain,
    ( subset('#skF_4','#skF_6')
    | ( intersection('#skF_8','#skF_9') = '#skF_7' ) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_128,plain,
    intersection('#skF_8','#skF_9') = '#skF_7',
    inference(splitLeft,[status(thm)],[c_68]) ).

tff(c_2,plain,
    ! [B_1,C_2] : subset(intersection(B_1,C_2),B_1),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_135,plain,
    subset('#skF_7','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_128,c_2]) ).

tff(c_79,plain,
    ! [C_30,B_31] : ( intersection(C_30,B_31) = intersection(B_31,C_30) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_94,plain,
    ! [C_30,B_31] : subset(intersection(C_30,B_31),B_31),
    inference(superposition,[status(thm),theory(equality)],[c_79,c_2]) ).

tff(c_132,plain,
    subset('#skF_7','#skF_9'),
    inference(superposition,[status(thm),theory(equality)],[c_128,c_94]) ).

tff(c_60,plain,
    ( subset('#skF_4','#skF_6')
    | subset('#skF_10','#skF_8')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_184,plain,
    ( subset('#skF_4','#skF_6')
    | subset('#skF_10','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_60]) ).

tff(c_185,plain,
    subset('#skF_10','#skF_8'),
    inference(splitLeft,[status(thm)],[c_184]) ).

tff(c_54,plain,
    ( subset('#skF_4','#skF_5')
    | subset('#skF_10','#skF_9')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_227,plain,
    ( subset('#skF_4','#skF_5')
    | subset('#skF_10','#skF_9') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_54]) ).

tff(c_228,plain,
    subset('#skF_10','#skF_9'),
    inference(splitLeft,[status(thm)],[c_227]) ).

tff(c_340,plain,
    ! [B_65,C_66,D_67] :
      ( subset(B_65,intersection(C_66,D_67))
      | ~ subset(B_65,D_67)
      | ~ subset(B_65,C_66) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_2070,plain,
    ! [B_97] :
      ( subset(B_97,'#skF_7')
      | ~ subset(B_97,'#skF_9')
      | ~ subset(B_97,'#skF_8') ),
    inference(superposition,[status(thm),theory(equality)],[c_128,c_340]) ).

tff(c_44,plain,
    ( subset('#skF_4','#skF_6')
    | ~ subset('#skF_10','#skF_7')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_316,plain,
    ( subset('#skF_4','#skF_6')
    | ~ subset('#skF_10','#skF_7') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_44]) ).

tff(c_317,plain,
    ~ subset('#skF_10','#skF_7'),
    inference(splitLeft,[status(thm)],[c_316]) ).

tff(c_2079,plain,
    ( ~ subset('#skF_10','#skF_9')
    | ~ subset('#skF_10','#skF_8') ),
    inference(resolution,[status(thm)],[c_2070,c_317]) ).

tff(c_2093,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_185,c_228,c_2079]) ).

tff(c_2094,plain,
    subset('#skF_4','#skF_6'),
    inference(splitRight,[status(thm)],[c_316]) ).

tff(c_2095,plain,
    subset('#skF_10','#skF_7'),
    inference(splitRight,[status(thm)],[c_316]) ).

tff(c_46,plain,
    ( subset('#skF_4','#skF_5')
    | ~ subset('#skF_10','#skF_7')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_2588,plain,
    subset('#skF_4','#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_2095,c_46]) ).

tff(c_4,plain,
    ! [B_3,C_4,D_5] :
      ( subset(B_3,intersection(C_4,D_5))
      | ~ subset(B_3,D_5)
      | ~ subset(B_3,C_4) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_24,plain,
    ! [C_17,B_16] : ( intersection(C_17,B_16) = intersection(B_16,C_17) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_40,plain,
    ( ( intersection('#skF_5','#skF_6') != '#skF_4' )
    | ~ subset('#skF_10','#skF_7')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_73,plain,
    ( ( intersection('#skF_6','#skF_5') != '#skF_4' )
    | ~ subset('#skF_10','#skF_7')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_40]) ).

tff(c_2852,plain,
    intersection('#skF_6','#skF_5') != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_2095,c_73]) ).

tff(c_42,plain,
    ! [E_25] :
      ( subset(E_25,'#skF_4')
      | ~ subset(E_25,'#skF_6')
      | ~ subset(E_25,'#skF_5')
      | ~ subset('#skF_10','#skF_7')
      | ~ subset('#skF_7','#skF_9')
      | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_3003,plain,
    ! [E_119] :
      ( subset(E_119,'#skF_4')
      | ~ subset(E_119,'#skF_6')
      | ~ subset(E_119,'#skF_5') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_2095,c_42]) ).

tff(c_4300,plain,
    ! [C_138] :
      ( subset(intersection(C_138,'#skF_5'),'#skF_4')
      | ~ subset(intersection(C_138,'#skF_5'),'#skF_6') ),
    inference(resolution,[status(thm)],[c_94,c_3003]) ).

tff(c_4344,plain,
    subset(intersection('#skF_6','#skF_5'),'#skF_4'),
    inference(resolution,[status(thm)],[c_2,c_4300]) ).

tff(c_18,plain,
    ! [C_15,B_14] :
      ( ( C_15 = B_14 )
      | ~ subset(C_15,B_14)
      | ~ subset(B_14,C_15) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_4352,plain,
    ( ( intersection('#skF_6','#skF_5') = '#skF_4' )
    | ~ subset('#skF_4',intersection('#skF_6','#skF_5')) ),
    inference(resolution,[status(thm)],[c_4344,c_18]) ).

tff(c_4357,plain,
    ~ subset('#skF_4',intersection('#skF_6','#skF_5')),
    inference(negUnitSimplification,[status(thm)],[c_2852,c_4352]) ).

tff(c_4360,plain,
    ( ~ subset('#skF_4','#skF_5')
    | ~ subset('#skF_4','#skF_6') ),
    inference(resolution,[status(thm)],[c_4,c_4357]) ).

tff(c_4364,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2094,c_2588,c_4360]) ).

tff(c_4366,plain,
    ~ subset('#skF_10','#skF_9'),
    inference(splitRight,[status(thm)],[c_227]) ).

tff(c_52,plain,
    ( subset('#skF_4','#skF_6')
    | subset('#skF_10','#skF_9')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_4932,plain,
    ( subset('#skF_4','#skF_6')
    | subset('#skF_10','#skF_9') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_52]) ).

tff(c_4933,plain,
    subset('#skF_4','#skF_6'),
    inference(negUnitSimplification,[status(thm)],[c_4366,c_4932]) ).

tff(c_4365,plain,
    subset('#skF_4','#skF_5'),
    inference(splitRight,[status(thm)],[c_227]) ).

tff(c_48,plain,
    ( ( intersection('#skF_5','#skF_6') != '#skF_4' )
    | subset('#skF_10','#skF_9')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_72,plain,
    ( ( intersection('#skF_6','#skF_5') != '#skF_4' )
    | subset('#skF_10','#skF_9')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_48]) ).

tff(c_6391,plain,
    ( ( intersection('#skF_6','#skF_5') != '#skF_4' )
    | subset('#skF_10','#skF_9') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_72]) ).

tff(c_6392,plain,
    intersection('#skF_6','#skF_5') != '#skF_4',
    inference(negUnitSimplification,[status(thm)],[c_4366,c_6391]) ).

tff(c_50,plain,
    ! [E_25] :
      ( subset(E_25,'#skF_4')
      | ~ subset(E_25,'#skF_6')
      | ~ subset(E_25,'#skF_5')
      | subset('#skF_10','#skF_9')
      | ~ subset('#skF_7','#skF_9')
      | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_5172,plain,
    ! [E_25] :
      ( subset(E_25,'#skF_4')
      | ~ subset(E_25,'#skF_6')
      | ~ subset(E_25,'#skF_5')
      | subset('#skF_10','#skF_9') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_50]) ).

tff(c_5174,plain,
    ! [E_171] :
      ( subset(E_171,'#skF_4')
      | ~ subset(E_171,'#skF_6')
      | ~ subset(E_171,'#skF_5') ),
    inference(negUnitSimplification,[status(thm)],[c_4366,c_5172]) ).

tff(c_7076,plain,
    ! [C_205] :
      ( subset(intersection('#skF_5',C_205),'#skF_4')
      | ~ subset(intersection('#skF_5',C_205),'#skF_6') ),
    inference(resolution,[status(thm)],[c_2,c_5174]) ).

tff(c_7103,plain,
    subset(intersection('#skF_5','#skF_6'),'#skF_4'),
    inference(resolution,[status(thm)],[c_94,c_7076]) ).

tff(c_7121,plain,
    subset(intersection('#skF_6','#skF_5'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_7103]) ).

tff(c_7129,plain,
    ( ( intersection('#skF_6','#skF_5') = '#skF_4' )
    | ~ subset('#skF_4',intersection('#skF_6','#skF_5')) ),
    inference(resolution,[status(thm)],[c_7121,c_18]) ).

tff(c_7134,plain,
    ~ subset('#skF_4',intersection('#skF_6','#skF_5')),
    inference(negUnitSimplification,[status(thm)],[c_6392,c_7129]) ).

tff(c_7137,plain,
    ( ~ subset('#skF_4','#skF_5')
    | ~ subset('#skF_4','#skF_6') ),
    inference(resolution,[status(thm)],[c_4,c_7134]) ).

tff(c_7141,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4933,c_4365,c_7137]) ).

tff(c_7142,plain,
    subset('#skF_4','#skF_6'),
    inference(splitRight,[status(thm)],[c_184]) ).

tff(c_7143,plain,
    ~ subset('#skF_10','#skF_8'),
    inference(splitRight,[status(thm)],[c_184]) ).

tff(c_62,plain,
    ( subset('#skF_4','#skF_5')
    | subset('#skF_10','#skF_8')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_7694,plain,
    ( subset('#skF_4','#skF_5')
    | subset('#skF_10','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_62]) ).

tff(c_7695,plain,
    subset('#skF_4','#skF_5'),
    inference(negUnitSimplification,[status(thm)],[c_7143,c_7694]) ).

tff(c_56,plain,
    ( ( intersection('#skF_5','#skF_6') != '#skF_4' )
    | subset('#skF_10','#skF_8')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_74,plain,
    ( ( intersection('#skF_6','#skF_5') != '#skF_4' )
    | subset('#skF_10','#skF_8')
    | ~ subset('#skF_7','#skF_9')
    | ~ subset('#skF_7','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_56]) ).

tff(c_9198,plain,
    ( ( intersection('#skF_6','#skF_5') != '#skF_4' )
    | subset('#skF_10','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_74]) ).

tff(c_9199,plain,
    intersection('#skF_6','#skF_5') != '#skF_4',
    inference(negUnitSimplification,[status(thm)],[c_7143,c_9198]) ).

tff(c_58,plain,
    ! [E_25] :
      ( subset(E_25,'#skF_4')
      | ~ subset(E_25,'#skF_6')
      | ~ subset(E_25,'#skF_5')
      | subset('#skF_10','#skF_8')
      | ~ subset('#skF_7','#skF_9')
      | ~ subset('#skF_7','#skF_8') ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_7845,plain,
    ! [E_25] :
      ( subset(E_25,'#skF_4')
      | ~ subset(E_25,'#skF_6')
      | ~ subset(E_25,'#skF_5')
      | subset('#skF_10','#skF_8') ),
    inference(demodulation,[status(thm),theory(equality)],[c_135,c_132,c_58]) ).

tff(c_7847,plain,
    ! [E_235] :
      ( subset(E_235,'#skF_4')
      | ~ subset(E_235,'#skF_6')
      | ~ subset(E_235,'#skF_5') ),
    inference(negUnitSimplification,[status(thm)],[c_7143,c_7845]) ).

tff(c_9976,plain,
    ! [C_277] :
      ( subset(intersection('#skF_5',C_277),'#skF_4')
      | ~ subset(intersection('#skF_5',C_277),'#skF_6') ),
    inference(resolution,[status(thm)],[c_2,c_7847]) ).

tff(c_10003,plain,
    subset(intersection('#skF_5','#skF_6'),'#skF_4'),
    inference(resolution,[status(thm)],[c_94,c_9976]) ).

tff(c_10021,plain,
    subset(intersection('#skF_6','#skF_5'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_10003]) ).

tff(c_10029,plain,
    ( ( intersection('#skF_6','#skF_5') = '#skF_4' )
    | ~ subset('#skF_4',intersection('#skF_6','#skF_5')) ),
    inference(resolution,[status(thm)],[c_10021,c_18]) ).

tff(c_10034,plain,
    ~ subset('#skF_4',intersection('#skF_6','#skF_5')),
    inference(negUnitSimplification,[status(thm)],[c_9199,c_10029]) ).

tff(c_10037,plain,
    ( ~ subset('#skF_4','#skF_5')
    | ~ subset('#skF_4','#skF_6') ),
    inference(resolution,[status(thm)],[c_4,c_10034]) ).

tff(c_10041,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7142,c_7695,c_10037]) ).

tff(c_10042,plain,
    subset('#skF_4','#skF_6'),
    inference(splitRight,[status(thm)],[c_68]) ).

tff(c_10043,plain,
    intersection('#skF_8','#skF_9') != '#skF_7',
    inference(splitRight,[status(thm)],[c_68]) ).

tff(c_70,plain,
    ( subset('#skF_4','#skF_5')
    | ( intersection('#skF_8','#skF_9') = '#skF_7' ) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_10044,plain,
    subset('#skF_4','#skF_5'),
    inference(negUnitSimplification,[status(thm)],[c_10043,c_70]) ).

tff(c_64,plain,
    ( ( intersection('#skF_5','#skF_6') != '#skF_4' )
    | ( intersection('#skF_8','#skF_9') = '#skF_7' ) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_71,plain,
    ( ( intersection('#skF_6','#skF_5') != '#skF_4' )
    | ( intersection('#skF_8','#skF_9') = '#skF_7' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_64]) ).

tff(c_10053,plain,
    intersection('#skF_6','#skF_5') != '#skF_4',
    inference(negUnitSimplification,[status(thm)],[c_10043,c_71]) ).

tff(c_66,plain,
    ! [E_25] :
      ( subset(E_25,'#skF_4')
      | ~ subset(E_25,'#skF_6')
      | ~ subset(E_25,'#skF_5')
      | ( intersection('#skF_8','#skF_9') = '#skF_7' ) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_11394,plain,
    ! [E_330] :
      ( subset(E_330,'#skF_4')
      | ~ subset(E_330,'#skF_6')
      | ~ subset(E_330,'#skF_5') ),
    inference(negUnitSimplification,[status(thm)],[c_10043,c_66]) ).

tff(c_11853,plain,
    ! [C_347] :
      ( subset(intersection('#skF_5',C_347),'#skF_4')
      | ~ subset(intersection('#skF_5',C_347),'#skF_6') ),
    inference(resolution,[status(thm)],[c_2,c_11394]) ).

tff(c_11880,plain,
    subset(intersection('#skF_5','#skF_6'),'#skF_4'),
    inference(resolution,[status(thm)],[c_94,c_11853]) ).

tff(c_11898,plain,
    subset(intersection('#skF_6','#skF_5'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_11880]) ).

tff(c_11906,plain,
    ( ( intersection('#skF_6','#skF_5') = '#skF_4' )
    | ~ subset('#skF_4',intersection('#skF_6','#skF_5')) ),
    inference(resolution,[status(thm)],[c_11898,c_18]) ).

tff(c_11911,plain,
    ~ subset('#skF_4',intersection('#skF_6','#skF_5')),
    inference(negUnitSimplification,[status(thm)],[c_10053,c_11906]) ).

tff(c_11914,plain,
    ( ~ subset('#skF_4','#skF_5')
    | ~ subset('#skF_4','#skF_6') ),
    inference(resolution,[status(thm)],[c_4,c_11911]) ).

tff(c_11918,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_10042,c_10044,c_11914]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SET598+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15  % 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
% 0.15/0.37  % Computer : n007.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 16:50:38 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 7.38/2.98  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.38/2.99  
% 7.38/2.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.38/3.03  
% 7.38/3.03  Inference rules
% 7.38/3.03  ----------------------
% 7.38/3.03  #Ref     : 0
% 7.38/3.03  #Sup     : 2899
% 7.38/3.03  #Fact    : 0
% 7.38/3.03  #Define  : 0
% 7.38/3.03  #Split   : 20
% 7.38/3.03  #Chain   : 0
% 7.38/3.03  #Close   : 0
% 7.38/3.03  
% 7.38/3.03  Ordering : KBO
% 7.38/3.03  
% 7.38/3.03  Simplification rules
% 7.38/3.03  ----------------------
% 7.38/3.03  #Subsume      : 438
% 7.38/3.03  #Demod        : 3129
% 7.38/3.03  #Tautology    : 1856
% 7.38/3.03  #SimpNegUnit  : 21
% 7.38/3.03  #BackRed      : 0
% 7.38/3.03  
% 7.38/3.03  #Partial instantiations: 0
% 7.38/3.03  #Strategies tried      : 1
% 7.38/3.03  
% 7.38/3.03  Timing (in seconds)
% 7.38/3.03  ----------------------
% 7.38/3.03  Preprocessing        : 0.50
% 7.38/3.03  Parsing              : 0.25
% 7.38/3.03  CNF conversion       : 0.04
% 7.38/3.03  Main loop            : 1.38
% 7.38/3.03  Inferencing          : 0.46
% 7.38/3.03  Reduction            : 0.55
% 7.38/3.03  Demodulation         : 0.44
% 7.38/3.03  BG Simplification    : 0.05
% 7.38/3.04  Subsumption          : 0.24
% 7.38/3.04  Abstraction          : 0.06
% 7.38/3.04  MUC search           : 0.00
% 7.38/3.04  Cooper               : 0.00
% 7.38/3.04  Total                : 1.95
% 7.38/3.04  Index Insertion      : 0.00
% 7.38/3.04  Index Deletion       : 0.00
% 7.38/3.04  Index Matching       : 0.00
% 7.38/3.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------