TSTP Solution File: SEU220+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU220+3 : 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 : n026.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 10:58:03 EDT 2023

% Result   : Theorem 18.12s 7.54s
% Output   : CNFRefutation 18.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  121 (  36 unt;  32 typ;   0 def)
%            Number of atoms       :  252 (  52 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  296 ( 133   ~; 115   |;  30   &)
%                                         (   1 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  21   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  11 con; 0-2 aty)
%            Number of variables   :   68 (;  65   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > relation_composition > apply > #nlpp > relation_rng > relation_dom > powerset > function_inverse > empty_set > #skF_4 > #skF_17 > #skF_11 > #skF_1 > #skF_8 > #skF_7 > #skF_13 > #skF_10 > #skF_16 > #skF_14 > #skF_12 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_9 > #skF_15

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff('#skF_1',type,
    '#skF_1': $i > $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_13',type,
    '#skF_13': ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_274,negated_conjecture,
    ~ ! [A,B] :
        ( ( relation(B)
          & function(B) )
       => ( ( one_to_one(B)
            & in(A,relation_rng(B)) )
         => ( ( A = apply(B,apply(function_inverse(B),A)) )
            & ( A = apply(relation_composition(function_inverse(B),B),A) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).

tff(f_59,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( relation(function_inverse(A))
        & function(function_inverse(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).

tff(f_251,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
       => ! [B] :
            ( ( relation(B)
              & function(B) )
           => ( ( B = function_inverse(A) )
            <=> ( ( relation_dom(B) = relation_rng(A) )
                & ! [C,D] :
                    ( ( ( in(C,relation_rng(A))
                        & ( D = apply(B,C) ) )
                     => ( in(D,relation_dom(A))
                        & ( C = apply(A,D) ) ) )
                    & ( ( in(D,relation_dom(A))
                        & ( C = apply(A,D) ) )
                     => ( in(C,relation_rng(A))
                        & ( D = apply(B,C) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).

tff(f_290,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

tff(f_144,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_285,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_161,axiom,
    ? [A] :
      ( relation(A)
      & empty(A)
      & function(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

tff(f_122,axiom,
    ! [A] :
      ( empty(A)
     => ( empty(relation_dom(A))
        & relation(relation_dom(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

tff(f_171,axiom,
    ! [A] :
    ? [B] :
      ( element(B,powerset(A))
      & empty(B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

tff(f_281,axiom,
    ! [A,B,C] :
      ~ ( in(A,B)
        & element(B,powerset(C))
        & empty(C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

tff(f_51,axiom,
    ! [A] :
      ( ( relation(A)
        & empty(A)
        & function(A) )
     => ( relation(A)
        & function(A)
        & one_to_one(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).

tff(f_128,axiom,
    ! [A] :
      ( empty(A)
     => ( empty(relation_rng(A))
        & relation(relation_rng(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

tff(f_261,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
       => ( ( relation_rng(A) = relation_dom(function_inverse(A)) )
          & ( relation_dom(A) = relation_rng(function_inverse(A)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).

tff(f_203,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( in(A,relation_dom(B))
           => ( apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).

tff(c_154,plain,
    relation('#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_152,plain,
    function('#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_150,plain,
    one_to_one('#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_16,plain,
    ! [A_6] :
      ( relation(function_inverse(A_6))
      | ~ function(A_6)
      | ~ relation(A_6) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_148,plain,
    in('#skF_16',relation_rng('#skF_17')),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_6668,plain,
    ! [A_355,C_356] :
      ( in(apply(function_inverse(A_355),C_356),relation_dom(A_355))
      | ~ in(C_356,relation_rng(A_355))
      | ~ function(function_inverse(A_355))
      | ~ relation(function_inverse(A_355))
      | ~ one_to_one(A_355)
      | ~ function(A_355)
      | ~ relation(A_355) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_160,plain,
    ! [B_64,A_63] :
      ( ~ empty(B_64)
      | ~ in(A_63,B_64) ),
    inference(cnfTransformation,[status(thm)],[f_290]) ).

tff(c_33107,plain,
    ! [A_596,C_597] :
      ( ~ empty(relation_dom(A_596))
      | ~ in(C_597,relation_rng(A_596))
      | ~ function(function_inverse(A_596))
      | ~ relation(function_inverse(A_596))
      | ~ one_to_one(A_596)
      | ~ function(A_596)
      | ~ relation(A_596) ),
    inference(resolution,[status(thm)],[c_6668,c_160]) ).

tff(c_33183,plain,
    ( ~ empty(relation_dom('#skF_17'))
    | ~ function(function_inverse('#skF_17'))
    | ~ relation(function_inverse('#skF_17'))
    | ~ one_to_one('#skF_17')
    | ~ function('#skF_17')
    | ~ relation('#skF_17') ),
    inference(resolution,[status(thm)],[c_148,c_33107]) ).

tff(c_33191,plain,
    ( ~ empty(relation_dom('#skF_17'))
    | ~ function(function_inverse('#skF_17'))
    | ~ relation(function_inverse('#skF_17')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_152,c_150,c_33183]) ).

tff(c_34039,plain,
    ~ relation(function_inverse('#skF_17')),
    inference(splitLeft,[status(thm)],[c_33191]) ).

tff(c_34042,plain,
    ( ~ function('#skF_17')
    | ~ relation('#skF_17') ),
    inference(resolution,[status(thm)],[c_16,c_34039]) ).

tff(c_34049,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_152,c_34042]) ).

tff(c_34051,plain,
    relation(function_inverse('#skF_17')),
    inference(splitRight,[status(thm)],[c_33191]) ).

tff(c_14,plain,
    ! [A_6] :
      ( function(function_inverse(A_6))
      | ~ function(A_6)
      | ~ relation(A_6) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_66,plain,
    empty('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_170,plain,
    ! [A_71] :
      ( ( empty_set = A_71 )
      | ~ empty(A_71) ),
    inference(cnfTransformation,[status(thm)],[f_285]) ).

tff(c_190,plain,
    empty_set = '#skF_3',
    inference(resolution,[status(thm)],[c_66,c_170]) ).

tff(c_76,plain,
    empty('#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_189,plain,
    empty_set = '#skF_6',
    inference(resolution,[status(thm)],[c_76,c_170]) ).

tff(c_3491,plain,
    '#skF_6' = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_189]) ).

tff(c_74,plain,
    function('#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_3505,plain,
    function('#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_3491,c_74]) ).

tff(c_3541,plain,
    ! [A_225] :
      ( empty(relation_dom(A_225))
      | ~ empty(A_225) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_158,plain,
    ! [A_62] :
      ( ( empty_set = A_62 )
      | ~ empty(A_62) ),
    inference(cnfTransformation,[status(thm)],[f_285]) ).

tff(c_192,plain,
    ! [A_62] :
      ( ( A_62 = '#skF_6' )
      | ~ empty(A_62) ),
    inference(demodulation,[status(thm),theory(equality)],[c_189,c_158]) ).

tff(c_3525,plain,
    ! [A_62] :
      ( ( A_62 = '#skF_3' )
      | ~ empty(A_62) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3491,c_192]) ).

tff(c_3560,plain,
    ! [A_228] :
      ( ( relation_dom(A_228) = '#skF_3' )
      | ~ empty(A_228) ),
    inference(resolution,[status(thm)],[c_3541,c_3525]) ).

tff(c_3572,plain,
    relation_dom('#skF_3') = '#skF_3',
    inference(resolution,[status(thm)],[c_66,c_3560]) ).

tff(c_64,plain,
    relation('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_84,plain,
    ! [A_24] : empty('#skF_8'(A_24)),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_186,plain,
    ! [A_24] : ( '#skF_8'(A_24) = empty_set ),
    inference(resolution,[status(thm)],[c_84,c_170]) ).

tff(c_3514,plain,
    ! [A_24] : ( '#skF_8'(A_24) = '#skF_3' ),
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_186]) ).

tff(c_86,plain,
    ! [A_24] : element('#skF_8'(A_24),powerset(A_24)),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_3532,plain,
    ! [A_24] : element('#skF_3',powerset(A_24)),
    inference(demodulation,[status(thm),theory(equality)],[c_3514,c_86]) ).

tff(c_4004,plain,
    ! [C_276,B_277,A_278] :
      ( ~ empty(C_276)
      | ~ element(B_277,powerset(C_276))
      | ~ in(A_278,B_277) ),
    inference(cnfTransformation,[status(thm)],[f_281]) ).

tff(c_4016,plain,
    ! [A_24,A_278] :
      ( ~ empty(A_24)
      | ~ in(A_278,'#skF_3') ),
    inference(resolution,[status(thm)],[c_3532,c_4004]) ).

tff(c_4018,plain,
    ! [A_278] : ~ in(A_278,'#skF_3'),
    inference(splitLeft,[status(thm)],[c_4016]) ).

tff(c_3826,plain,
    ! [A_252] :
      ( one_to_one(A_252)
      | ~ function(A_252)
      | ~ empty(A_252)
      | ~ relation(A_252) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_3844,plain,
    ( one_to_one('#skF_3')
    | ~ function('#skF_3')
    | ~ empty('#skF_3') ),
    inference(resolution,[status(thm)],[c_64,c_3826]) ).

tff(c_3866,plain,
    one_to_one('#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_3505,c_3844]) ).

tff(c_3551,plain,
    ! [A_227] :
      ( empty(relation_rng(A_227))
      | ~ empty(A_227) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_3587,plain,
    ! [A_229] :
      ( ( relation_rng(A_229) = '#skF_3' )
      | ~ empty(A_229) ),
    inference(resolution,[status(thm)],[c_3551,c_3525]) ).

tff(c_3599,plain,
    relation_rng('#skF_3') = '#skF_3',
    inference(resolution,[status(thm)],[c_66,c_3587]) ).

tff(c_9010,plain,
    ! [A_392,B_393] :
      ( in('#skF_13'(A_392,B_393),relation_dom(A_392))
      | in('#skF_14'(A_392,B_393),relation_rng(A_392))
      | ( function_inverse(A_392) = B_393 )
      | ( relation_rng(A_392) != relation_dom(B_393) )
      | ~ function(B_393)
      | ~ relation(B_393)
      | ~ one_to_one(A_392)
      | ~ function(A_392)
      | ~ relation(A_392) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_9045,plain,
    ! [B_393] :
      ( in('#skF_13'('#skF_3',B_393),'#skF_3')
      | in('#skF_14'('#skF_3',B_393),relation_rng('#skF_3'))
      | ( function_inverse('#skF_3') = B_393 )
      | ( relation_rng('#skF_3') != relation_dom(B_393) )
      | ~ function(B_393)
      | ~ relation(B_393)
      | ~ one_to_one('#skF_3')
      | ~ function('#skF_3')
      | ~ relation('#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_3572,c_9010]) ).

tff(c_9058,plain,
    ! [B_393] :
      ( in('#skF_13'('#skF_3',B_393),'#skF_3')
      | in('#skF_14'('#skF_3',B_393),'#skF_3')
      | ( function_inverse('#skF_3') = B_393 )
      | ( relation_dom(B_393) != '#skF_3' )
      | ~ function(B_393)
      | ~ relation(B_393) ),
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_3505,c_3866,c_3599,c_3599,c_9045]) ).

tff(c_21049,plain,
    ! [B_494] :
      ( ( function_inverse('#skF_3') = B_494 )
      | ( relation_dom(B_494) != '#skF_3' )
      | ~ function(B_494)
      | ~ relation(B_494) ),
    inference(negUnitSimplification,[status(thm)],[c_4018,c_4018,c_9058]) ).

tff(c_21076,plain,
    ( ( function_inverse('#skF_3') = '#skF_3' )
    | ( relation_dom('#skF_3') != '#skF_3' )
    | ~ function('#skF_3') ),
    inference(resolution,[status(thm)],[c_64,c_21049]) ).

tff(c_21101,plain,
    function_inverse('#skF_3') = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_3505,c_3572,c_21076]) ).

tff(c_9059,plain,
    ! [B_393] :
      ( ( function_inverse('#skF_3') = B_393 )
      | ( relation_dom(B_393) != '#skF_3' )
      | ~ function(B_393)
      | ~ relation(B_393) ),
    inference(negUnitSimplification,[status(thm)],[c_4018,c_4018,c_9058]) ).

tff(c_21111,plain,
    ! [B_393] :
      ( ( B_393 = '#skF_3' )
      | ( relation_dom(B_393) != '#skF_3' )
      | ~ function(B_393)
      | ~ relation(B_393) ),
    inference(demodulation,[status(thm),theory(equality)],[c_21101,c_9059]) ).

tff(c_34073,plain,
    ( ( function_inverse('#skF_17') = '#skF_3' )
    | ( relation_dom(function_inverse('#skF_17')) != '#skF_3' )
    | ~ function(function_inverse('#skF_17')) ),
    inference(resolution,[status(thm)],[c_34051,c_21111]) ).

tff(c_45790,plain,
    ~ function(function_inverse('#skF_17')),
    inference(splitLeft,[status(thm)],[c_34073]) ).

tff(c_45872,plain,
    ( ~ function('#skF_17')
    | ~ relation('#skF_17') ),
    inference(resolution,[status(thm)],[c_14,c_45790]) ).

tff(c_45879,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_152,c_45872]) ).

tff(c_45881,plain,
    function(function_inverse('#skF_17')),
    inference(splitRight,[status(thm)],[c_34073]) ).

tff(c_3415,plain,
    ! [A_213,C_214] :
      ( ( apply(A_213,apply(function_inverse(A_213),C_214)) = C_214 )
      | ~ in(C_214,relation_rng(A_213))
      | ~ function(function_inverse(A_213))
      | ~ relation(function_inverse(A_213))
      | ~ one_to_one(A_213)
      | ~ function(A_213)
      | ~ relation(A_213) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_146,plain,
    ( ( apply(relation_composition(function_inverse('#skF_17'),'#skF_17'),'#skF_16') != '#skF_16' )
    | ( apply('#skF_17',apply(function_inverse('#skF_17'),'#skF_16')) != '#skF_16' ) ),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_202,plain,
    apply('#skF_17',apply(function_inverse('#skF_17'),'#skF_16')) != '#skF_16',
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_3435,plain,
    ( ~ in('#skF_16',relation_rng('#skF_17'))
    | ~ function(function_inverse('#skF_17'))
    | ~ relation(function_inverse('#skF_17'))
    | ~ one_to_one('#skF_17')
    | ~ function('#skF_17')
    | ~ relation('#skF_17') ),
    inference(superposition,[status(thm),theory(equality)],[c_3415,c_202]) ).

tff(c_3450,plain,
    ( ~ function(function_inverse('#skF_17'))
    | ~ relation(function_inverse('#skF_17')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_152,c_150,c_148,c_3435]) ).

tff(c_3453,plain,
    ~ relation(function_inverse('#skF_17')),
    inference(splitLeft,[status(thm)],[c_3450]) ).

tff(c_3456,plain,
    ( ~ function('#skF_17')
    | ~ relation('#skF_17') ),
    inference(resolution,[status(thm)],[c_16,c_3453]) ).

tff(c_3463,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_152,c_3456]) ).

tff(c_3464,plain,
    ~ function(function_inverse('#skF_17')),
    inference(splitRight,[status(thm)],[c_3450]) ).

tff(c_3481,plain,
    ( ~ function('#skF_17')
    | ~ relation('#skF_17') ),
    inference(resolution,[status(thm)],[c_14,c_3464]) ).

tff(c_3488,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_152,c_3481]) ).

tff(c_3490,plain,
    apply('#skF_17',apply(function_inverse('#skF_17'),'#skF_16')) = '#skF_16',
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_144,plain,
    ! [A_58] :
      ( ( relation_dom(function_inverse(A_58)) = relation_rng(A_58) )
      | ~ one_to_one(A_58)
      | ~ function(A_58)
      | ~ relation(A_58) ),
    inference(cnfTransformation,[status(thm)],[f_261]) ).

tff(c_5327,plain,
    ! [B_322,C_323,A_324] :
      ( ( apply(relation_composition(B_322,C_323),A_324) = apply(C_323,apply(B_322,A_324)) )
      | ~ in(A_324,relation_dom(B_322))
      | ~ function(C_323)
      | ~ relation(C_323)
      | ~ function(B_322)
      | ~ relation(B_322) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_50088,plain,
    ! [A_807,C_808,A_809] :
      ( ( apply(relation_composition(function_inverse(A_807),C_808),A_809) = apply(C_808,apply(function_inverse(A_807),A_809)) )
      | ~ in(A_809,relation_rng(A_807))
      | ~ function(C_808)
      | ~ relation(C_808)
      | ~ function(function_inverse(A_807))
      | ~ relation(function_inverse(A_807))
      | ~ one_to_one(A_807)
      | ~ function(A_807)
      | ~ relation(A_807) ),
    inference(superposition,[status(thm),theory(equality)],[c_144,c_5327]) ).

tff(c_3489,plain,
    apply(relation_composition(function_inverse('#skF_17'),'#skF_17'),'#skF_16') != '#skF_16',
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_50132,plain,
    ( ( apply('#skF_17',apply(function_inverse('#skF_17'),'#skF_16')) != '#skF_16' )
    | ~ in('#skF_16',relation_rng('#skF_17'))
    | ~ function('#skF_17')
    | ~ relation('#skF_17')
    | ~ function(function_inverse('#skF_17'))
    | ~ relation(function_inverse('#skF_17'))
    | ~ one_to_one('#skF_17')
    | ~ function('#skF_17')
    | ~ relation('#skF_17') ),
    inference(superposition,[status(thm),theory(equality)],[c_50088,c_3489]) ).

tff(c_50197,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_152,c_150,c_34051,c_45881,c_154,c_152,c_148,c_3490,c_50132]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU220+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % 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 : n026.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 11:52:31 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 18.12/7.54  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.12/7.55  
% 18.12/7.55  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.12/7.59  
% 18.12/7.59  Inference rules
% 18.12/7.59  ----------------------
% 18.12/7.59  #Ref     : 0
% 18.12/7.59  #Sup     : 12759
% 18.12/7.59  #Fact    : 0
% 18.12/7.59  #Define  : 0
% 18.12/7.59  #Split   : 33
% 18.12/7.59  #Chain   : 0
% 18.12/7.59  #Close   : 0
% 18.12/7.59  
% 18.12/7.59  Ordering : KBO
% 18.12/7.59  
% 18.12/7.59  Simplification rules
% 18.12/7.59  ----------------------
% 18.12/7.59  #Subsume      : 3025
% 18.12/7.59  #Demod        : 11184
% 18.12/7.59  #Tautology    : 5635
% 18.12/7.59  #SimpNegUnit  : 107
% 18.12/7.59  #BackRed      : 19
% 18.12/7.59  
% 18.12/7.59  #Partial instantiations: 0
% 18.12/7.59  #Strategies tried      : 1
% 18.12/7.59  
% 18.12/7.59  Timing (in seconds)
% 18.12/7.59  ----------------------
% 18.12/7.60  Preprocessing        : 0.66
% 18.12/7.60  Parsing              : 0.34
% 18.12/7.60  CNF conversion       : 0.06
% 18.12/7.60  Main loop            : 5.84
% 18.12/7.60  Inferencing          : 1.30
% 18.12/7.60  Reduction            : 2.05
% 18.12/7.60  Demodulation         : 1.56
% 18.12/7.60  BG Simplification    : 0.12
% 18.12/7.60  Subsumption          : 2.06
% 18.12/7.60  Abstraction          : 0.14
% 18.12/7.60  MUC search           : 0.00
% 18.12/7.60  Cooper               : 0.00
% 18.12/7.60  Total                : 6.57
% 18.12/7.60  Index Insertion      : 0.00
% 18.12/7.60  Index Deletion       : 0.00
% 18.12/7.60  Index Matching       : 0.00
% 18.12/7.60  BG Taut test         : 0.00
%------------------------------------------------------------------------------