TSTP Solution File: SEU317+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n014.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 10:58:24 EDT 2023

% Result   : Theorem 22.07s 9.97s
% Output   : CNFRefutation 22.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   43
% Syntax   : Number of formulae    :  110 (  22 unt;  31 typ;   0 def)
%            Number of atoms       :  199 (   5 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  206 (  86   ~;  96   |;  10   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  25   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :  111 (; 109   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > closed_subset > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > top_str > one_sorted_str > natural > empty > topstr_closure > #nlpp > the_carrier > powerset > empty_set > #skF_7 > #skF_4 > #skF_10 > #skF_5 > #skF_2 > #skF_3 > #skF_9 > #skF_8 > #skF_1 > #skF_6

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_7',type,
    '#skF_7': $i > $i ).

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

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

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

tff(v1_int_1,type,
    v1_int_1: $i > $o ).

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

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

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

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

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

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

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

tff(v3_membered,type,
    v3_membered: $i > $o ).

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

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

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

tff(v1_xreal_0,type,
    v1_xreal_0: $i > $o ).

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

tff(v5_membered,type,
    v5_membered: $i > $o ).

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

tff(v2_membered,type,
    v2_membered: $i > $o ).

tff(v1_membered,type,
    v1_membered: $i > $o ).

tff(v1_xcmplx_0,type,
    v1_xcmplx_0: $i > $o ).

tff(v1_rat_1,type,
    v1_rat_1: $i > $o ).

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

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

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

tff(v4_membered,type,
    v4_membered: $i > $o ).

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

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

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

tff(f_194,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

tff(f_176,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_300,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

tff(f_278,negated_conjecture,
    ~ ! [A] :
        ( top_str(A)
       => ! [B] :
            ( element(B,powerset(the_carrier(A)))
           => subset(B,topstr_closure(A,B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).

tff(f_251,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

tff(f_247,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(f_235,axiom,
    ! [A] :
    ? [B] :
      ( element(B,powerset(A))
      & empty(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

tff(f_295,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_291,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

tff(f_241,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

tff(f_270,axiom,
    ! [A] :
      ( top_str(A)
     => ! [B] :
          ( element(B,powerset(the_carrier(A)))
         => ! [C] :
              ( in(C,the_carrier(A))
             => ( in(C,topstr_closure(A,B))
              <=> ! [D] :
                    ( element(D,powerset(the_carrier(A)))
                   => ( ( closed_subset(D,A)
                        & subset(B,D) )
                     => in(C,D) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).

tff(f_208,axiom,
    ( empty(empty_set)
    & v1_membered(empty_set)
    & v2_membered(empty_set)
    & v3_membered(empty_set)
    & v4_membered(empty_set)
    & v5_membered(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).

tff(c_106,plain,
    ! [A_46] : element('#skF_4'(A_46),A_46),
    inference(cnfTransformation,[status(thm)],[f_194]) ).

tff(c_1250,plain,
    ! [A_240,B_241] :
      ( in('#skF_1'(A_240,B_241),A_240)
      | subset(A_240,B_241) ),
    inference(cnfTransformation,[status(thm)],[f_176]) ).

tff(c_174,plain,
    ! [B_92,A_91] :
      ( ~ empty(B_92)
      | ~ in(A_91,B_92) ),
    inference(cnfTransformation,[status(thm)],[f_300]) ).

tff(c_1268,plain,
    ! [A_242,B_243] :
      ( ~ empty(A_242)
      | subset(A_242,B_243) ),
    inference(resolution,[status(thm)],[c_1250,c_174]) ).

tff(c_162,plain,
    ~ subset('#skF_10',topstr_closure('#skF_9','#skF_10')),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_1300,plain,
    ~ empty('#skF_10'),
    inference(resolution,[status(thm)],[c_1268,c_162]) ).

tff(c_164,plain,
    element('#skF_10',powerset(the_carrier('#skF_9'))),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_591,plain,
    ! [A_172,B_173] :
      ( subset(A_172,B_173)
      | ~ element(A_172,powerset(B_173)) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_608,plain,
    subset('#skF_10',the_carrier('#skF_9')),
    inference(resolution,[status(thm)],[c_164,c_591]) ).

tff(c_146,plain,
    ! [A_57,B_58] :
      ( in(A_57,B_58)
      | empty(B_58)
      | ~ element(A_57,B_58) ),
    inference(cnfTransformation,[status(thm)],[f_247]) ).

tff(c_1800,plain,
    ! [C_289,B_290,A_291] :
      ( in(C_289,B_290)
      | ~ in(C_289,A_291)
      | ~ subset(A_291,B_290) ),
    inference(cnfTransformation,[status(thm)],[f_176]) ).

tff(c_61403,plain,
    ! [A_1451,B_1452,B_1453] :
      ( in(A_1451,B_1452)
      | ~ subset(B_1453,B_1452)
      | empty(B_1453)
      | ~ element(A_1451,B_1453) ),
    inference(resolution,[status(thm)],[c_146,c_1800]) ).

tff(c_61415,plain,
    ! [A_1451] :
      ( in(A_1451,the_carrier('#skF_9'))
      | empty('#skF_10')
      | ~ element(A_1451,'#skF_10') ),
    inference(resolution,[status(thm)],[c_608,c_61403]) ).

tff(c_61427,plain,
    ! [A_1451] :
      ( in(A_1451,the_carrier('#skF_9'))
      | ~ element(A_1451,'#skF_10') ),
    inference(negUnitSimplification,[status(thm)],[c_1300,c_61415]) ).

tff(c_138,plain,
    ! [A_51] : empty('#skF_7'(A_51)),
    inference(cnfTransformation,[status(thm)],[f_235]) ).

tff(c_209,plain,
    ! [A_105] :
      ( ( empty_set = A_105 )
      | ~ empty(A_105) ),
    inference(cnfTransformation,[status(thm)],[f_295]) ).

tff(c_216,plain,
    ! [A_51] : ( '#skF_7'(A_51) = empty_set ),
    inference(resolution,[status(thm)],[c_138,c_209]) ).

tff(c_140,plain,
    ! [A_51] : element('#skF_7'(A_51),powerset(A_51)),
    inference(cnfTransformation,[status(thm)],[f_235]) ).

tff(c_274,plain,
    ! [A_51] : element(empty_set,powerset(A_51)),
    inference(demodulation,[status(thm),theory(equality)],[c_216,c_140]) ).

tff(c_1758,plain,
    ! [C_283,B_284,A_285] :
      ( ~ empty(C_283)
      | ~ element(B_284,powerset(C_283))
      | ~ in(A_285,B_284) ),
    inference(cnfTransformation,[status(thm)],[f_291]) ).

tff(c_1772,plain,
    ! [A_51,A_285] :
      ( ~ empty(A_51)
      | ~ in(A_285,empty_set) ),
    inference(resolution,[status(thm)],[c_274,c_1758]) ).

tff(c_1775,plain,
    ! [A_285] : ~ in(A_285,empty_set),
    inference(splitLeft,[status(thm)],[c_1772]) ).

tff(c_166,plain,
    top_str('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_144,plain,
    ! [A_55,B_56] :
      ( element(A_55,B_56)
      | ~ in(A_55,B_56) ),
    inference(cnfTransformation,[status(thm)],[f_241]) ).

tff(c_1265,plain,
    ! [A_240,B_241] :
      ( element('#skF_1'(A_240,B_241),A_240)
      | subset(A_240,B_241) ),
    inference(resolution,[status(thm)],[c_1250,c_144]) ).

tff(c_2449,plain,
    ! [A_322,B_323,C_324] :
      ( closed_subset('#skF_8'(A_322,B_323,C_324),A_322)
      | in(C_324,topstr_closure(A_322,B_323))
      | ~ in(C_324,the_carrier(A_322))
      | ~ element(B_323,powerset(the_carrier(A_322)))
      | ~ top_str(A_322) ),
    inference(cnfTransformation,[status(thm)],[f_270]) ).

tff(c_2468,plain,
    ! [C_324] :
      ( closed_subset('#skF_8'('#skF_9','#skF_10',C_324),'#skF_9')
      | in(C_324,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_324,the_carrier('#skF_9'))
      | ~ top_str('#skF_9') ),
    inference(resolution,[status(thm)],[c_164,c_2449]) ).

tff(c_2489,plain,
    ! [C_325] :
      ( closed_subset('#skF_8'('#skF_9','#skF_10',C_325),'#skF_9')
      | in(C_325,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_325,the_carrier('#skF_9')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_2468]) ).

tff(c_2515,plain,
    ! [C_325] :
      ( ~ empty(topstr_closure('#skF_9','#skF_10'))
      | closed_subset('#skF_8'('#skF_9','#skF_10',C_325),'#skF_9')
      | ~ in(C_325,the_carrier('#skF_9')) ),
    inference(resolution,[status(thm)],[c_2489,c_174]) ).

tff(c_2667,plain,
    ~ empty(topstr_closure('#skF_9','#skF_10')),
    inference(splitLeft,[status(thm)],[c_2515]) ).

tff(c_3033,plain,
    ! [A_371,B_372,B_373] :
      ( in(A_371,B_372)
      | ~ subset(B_373,B_372)
      | empty(B_373)
      | ~ element(A_371,B_373) ),
    inference(resolution,[status(thm)],[c_146,c_1800]) ).

tff(c_3047,plain,
    ! [A_371] :
      ( in(A_371,the_carrier('#skF_9'))
      | empty('#skF_10')
      | ~ element(A_371,'#skF_10') ),
    inference(resolution,[status(thm)],[c_608,c_3033]) ).

tff(c_3062,plain,
    ! [A_371] :
      ( in(A_371,the_carrier('#skF_9'))
      | ~ element(A_371,'#skF_10') ),
    inference(negUnitSimplification,[status(thm)],[c_1300,c_3047]) ).

tff(c_2077,plain,
    ! [B_300,A_301,C_302] :
      ( subset(B_300,'#skF_8'(A_301,B_300,C_302))
      | in(C_302,topstr_closure(A_301,B_300))
      | ~ in(C_302,the_carrier(A_301))
      | ~ element(B_300,powerset(the_carrier(A_301)))
      | ~ top_str(A_301) ),
    inference(cnfTransformation,[status(thm)],[f_270]) ).

tff(c_2093,plain,
    ! [C_302] :
      ( subset('#skF_10','#skF_8'('#skF_9','#skF_10',C_302))
      | in(C_302,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_302,the_carrier('#skF_9'))
      | ~ top_str('#skF_9') ),
    inference(resolution,[status(thm)],[c_164,c_2077]) ).

tff(c_2102,plain,
    ! [C_302] :
      ( subset('#skF_10','#skF_8'('#skF_9','#skF_10',C_302))
      | in(C_302,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_302,the_carrier('#skF_9')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_2093]) ).

tff(c_3037,plain,
    ! [A_371,C_302] :
      ( in(A_371,'#skF_8'('#skF_9','#skF_10',C_302))
      | empty('#skF_10')
      | ~ element(A_371,'#skF_10')
      | in(C_302,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_302,the_carrier('#skF_9')) ),
    inference(resolution,[status(thm)],[c_2102,c_3033]) ).

tff(c_3191,plain,
    ! [A_377,C_378] :
      ( in(A_377,'#skF_8'('#skF_9','#skF_10',C_378))
      | ~ element(A_377,'#skF_10')
      | in(C_378,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_378,the_carrier('#skF_9')) ),
    inference(negUnitSimplification,[status(thm)],[c_1300,c_3037]) ).

tff(c_154,plain,
    ! [C_79,A_61,B_73] :
      ( ~ in(C_79,'#skF_8'(A_61,B_73,C_79))
      | in(C_79,topstr_closure(A_61,B_73))
      | ~ in(C_79,the_carrier(A_61))
      | ~ element(B_73,powerset(the_carrier(A_61)))
      | ~ top_str(A_61) ),
    inference(cnfTransformation,[status(thm)],[f_270]) ).

tff(c_3196,plain,
    ! [C_378] :
      ( ~ element('#skF_10',powerset(the_carrier('#skF_9')))
      | ~ top_str('#skF_9')
      | ~ element(C_378,'#skF_10')
      | in(C_378,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_378,the_carrier('#skF_9')) ),
    inference(resolution,[status(thm)],[c_3191,c_154]) ).

tff(c_30039,plain,
    ! [C_1053] :
      ( ~ element(C_1053,'#skF_10')
      | in(C_1053,topstr_closure('#skF_9','#skF_10'))
      | ~ in(C_1053,the_carrier('#skF_9')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_164,c_3196]) ).

tff(c_50089,plain,
    ! [C_1284] :
      ( element(C_1284,topstr_closure('#skF_9','#skF_10'))
      | ~ element(C_1284,'#skF_10')
      | ~ in(C_1284,the_carrier('#skF_9')) ),
    inference(resolution,[status(thm)],[c_30039,c_144]) ).

tff(c_50140,plain,
    ! [A_1285] :
      ( element(A_1285,topstr_closure('#skF_9','#skF_10'))
      | ~ element(A_1285,'#skF_10') ),
    inference(resolution,[status(thm)],[c_3062,c_50089]) ).

tff(c_1209,plain,
    ! [A_234,B_235] :
      ( in(A_234,B_235)
      | empty(B_235)
      | ~ element(A_234,B_235) ),
    inference(cnfTransformation,[status(thm)],[f_247]) ).

tff(c_84,plain,
    ! [A_38,B_39] :
      ( ~ in('#skF_1'(A_38,B_39),B_39)
      | subset(A_38,B_39) ),
    inference(cnfTransformation,[status(thm)],[f_176]) ).

tff(c_1222,plain,
    ! [A_38,B_235] :
      ( subset(A_38,B_235)
      | empty(B_235)
      | ~ element('#skF_1'(A_38,B_235),B_235) ),
    inference(resolution,[status(thm)],[c_1209,c_84]) ).

tff(c_50194,plain,
    ! [A_38] :
      ( subset(A_38,topstr_closure('#skF_9','#skF_10'))
      | empty(topstr_closure('#skF_9','#skF_10'))
      | ~ element('#skF_1'(A_38,topstr_closure('#skF_9','#skF_10')),'#skF_10') ),
    inference(resolution,[status(thm)],[c_50140,c_1222]) ).

tff(c_60870,plain,
    ! [A_1403] :
      ( subset(A_1403,topstr_closure('#skF_9','#skF_10'))
      | ~ element('#skF_1'(A_1403,topstr_closure('#skF_9','#skF_10')),'#skF_10') ),
    inference(negUnitSimplification,[status(thm)],[c_2667,c_50194]) ).

tff(c_60997,plain,
    subset('#skF_10',topstr_closure('#skF_9','#skF_10')),
    inference(resolution,[status(thm)],[c_1265,c_60870]) ).

tff(c_61008,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_162,c_162,c_60997]) ).

tff(c_61010,plain,
    empty(topstr_closure('#skF_9','#skF_10')),
    inference(splitRight,[status(thm)],[c_2515]) ).

tff(c_172,plain,
    ! [A_90] :
      ( ( empty_set = A_90 )
      | ~ empty(A_90) ),
    inference(cnfTransformation,[status(thm)],[f_295]) ).

tff(c_61017,plain,
    topstr_closure('#skF_9','#skF_10') = empty_set,
    inference(resolution,[status(thm)],[c_61010,c_172]) ).

tff(c_61020,plain,
    ! [C_302] :
      ( subset('#skF_10','#skF_8'('#skF_9','#skF_10',C_302))
      | in(C_302,empty_set)
      | ~ in(C_302,the_carrier('#skF_9')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_61017,c_2102]) ).

tff(c_62626,plain,
    ! [C_1534] :
      ( subset('#skF_10','#skF_8'('#skF_9','#skF_10',C_1534))
      | ~ in(C_1534,the_carrier('#skF_9')) ),
    inference(negUnitSimplification,[status(thm)],[c_1775,c_61020]) ).

tff(c_1806,plain,
    ! [A_57,B_290,B_58] :
      ( in(A_57,B_290)
      | ~ subset(B_58,B_290)
      | empty(B_58)
      | ~ element(A_57,B_58) ),
    inference(resolution,[status(thm)],[c_146,c_1800]) ).

tff(c_62630,plain,
    ! [A_57,C_1534] :
      ( in(A_57,'#skF_8'('#skF_9','#skF_10',C_1534))
      | empty('#skF_10')
      | ~ element(A_57,'#skF_10')
      | ~ in(C_1534,the_carrier('#skF_9')) ),
    inference(resolution,[status(thm)],[c_62626,c_1806]) ).

tff(c_62952,plain,
    ! [A_1551,C_1552] :
      ( in(A_1551,'#skF_8'('#skF_9','#skF_10',C_1552))
      | ~ element(A_1551,'#skF_10')
      | ~ in(C_1552,the_carrier('#skF_9')) ),
    inference(negUnitSimplification,[status(thm)],[c_1300,c_62630]) ).

tff(c_63126,plain,
    ! [A_1558,A_1559] :
      ( in(A_1558,'#skF_8'('#skF_9','#skF_10',A_1559))
      | ~ element(A_1558,'#skF_10')
      | ~ element(A_1559,'#skF_10') ),
    inference(resolution,[status(thm)],[c_61427,c_62952]) ).

tff(c_63135,plain,
    ! [A_1559] :
      ( in(A_1559,topstr_closure('#skF_9','#skF_10'))
      | ~ in(A_1559,the_carrier('#skF_9'))
      | ~ element('#skF_10',powerset(the_carrier('#skF_9')))
      | ~ top_str('#skF_9')
      | ~ element(A_1559,'#skF_10') ),
    inference(resolution,[status(thm)],[c_63126,c_154]) ).

tff(c_63159,plain,
    ! [A_1559] :
      ( in(A_1559,empty_set)
      | ~ in(A_1559,the_carrier('#skF_9'))
      | ~ element(A_1559,'#skF_10') ),
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_164,c_61017,c_63135]) ).

tff(c_63267,plain,
    ! [A_1562] :
      ( ~ in(A_1562,the_carrier('#skF_9'))
      | ~ element(A_1562,'#skF_10') ),
    inference(negUnitSimplification,[status(thm)],[c_1775,c_63159]) ).

tff(c_63289,plain,
    ! [A_1563] : ~ element(A_1563,'#skF_10'),
    inference(resolution,[status(thm)],[c_61427,c_63267]) ).

tff(c_63299,plain,
    $false,
    inference(resolution,[status(thm)],[c_106,c_63289]) ).

tff(c_63300,plain,
    ! [A_51] : ~ empty(A_51),
    inference(splitRight,[status(thm)],[c_1772]) ).

tff(c_120,plain,
    empty(empty_set),
    inference(cnfTransformation,[status(thm)],[f_208]) ).

tff(c_63321,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_63300,c_120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 11:29:48 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 22.07/9.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.07/9.98  
% 22.07/9.98  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.07/10.01  
% 22.07/10.01  Inference rules
% 22.07/10.01  ----------------------
% 22.07/10.01  #Ref     : 0
% 22.07/10.01  #Sup     : 14590
% 22.07/10.01  #Fact    : 0
% 22.07/10.01  #Define  : 0
% 22.07/10.01  #Split   : 125
% 22.07/10.01  #Chain   : 0
% 22.07/10.01  #Close   : 0
% 22.07/10.01  
% 22.07/10.01  Ordering : KBO
% 22.07/10.01  
% 22.07/10.01  Simplification rules
% 22.07/10.01  ----------------------
% 22.07/10.01  #Subsume      : 8679
% 22.07/10.01  #Demod        : 4653
% 22.07/10.01  #Tautology    : 3171
% 22.07/10.01  #SimpNegUnit  : 2854
% 22.07/10.01  #BackRed      : 1059
% 22.07/10.01  
% 22.07/10.01  #Partial instantiations: 0
% 22.07/10.01  #Strategies tried      : 1
% 22.07/10.01  
% 22.07/10.01  Timing (in seconds)
% 22.07/10.01  ----------------------
% 22.07/10.01  Preprocessing        : 0.58
% 22.07/10.01  Parsing              : 0.31
% 22.07/10.01  CNF conversion       : 0.05
% 22.07/10.01  Main loop            : 8.36
% 22.07/10.01  Inferencing          : 1.90
% 22.07/10.01  Reduction            : 2.71
% 22.07/10.01  Demodulation         : 1.65
% 22.07/10.01  BG Simplification    : 0.08
% 22.07/10.01  Subsumption          : 3.17
% 22.07/10.01  Abstraction          : 0.12
% 22.07/10.01  MUC search           : 0.00
% 22.07/10.02  Cooper               : 0.00
% 22.07/10.02  Total                : 9.00
% 22.07/10.02  Index Insertion      : 0.00
% 22.07/10.02  Index Deletion       : 0.00
% 22.07/10.02  Index Matching       : 0.00
% 22.07/10.02  BG Taut test         : 0.00
%------------------------------------------------------------------------------