TSTP Solution File: SEU156+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU156+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/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 : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:57:49 EDT 2023

% Result   : Theorem 245.71s 198.22s
% Output   : CNFRefutation 245.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  134 (  72 unt;  11 typ;   0 def)
%            Number of atoms       :  198 ( 192 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  136 (  61   ~;  69   |;   3   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  179 (; 179   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > empty > unordered_pair > ordered_pair > #nlpp > singleton > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

tff(f_58,axiom,
    ! [A] : ( unordered_pair(A,A) = singleton(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

tff(f_30,axiom,
    ! [A,B] : ( ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

tff(f_28,axiom,
    ! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

tff(f_56,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( ordered_pair(A,B) = ordered_pair(C,D) )
       => ( ( A = C )
          & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).

tff(f_49,axiom,
    ! [A,B,C,D] :
      ~ ( ( unordered_pair(A,B) = unordered_pair(C,D) )
        & ( A != C )
        & ( A != D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).

tff(f_66,axiom,
    ! [A,B,C] :
      ( ( singleton(A) = unordered_pair(B,C) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).

tff(f_70,axiom,
    ! [A,B,C] :
      ( ( singleton(A) = unordered_pair(B,C) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).

tff(c_20,plain,
    ! [A_13] : ( unordered_pair(A_13,A_13) = singleton(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_15751,plain,
    ! [A_386,B_387] : ( unordered_pair(unordered_pair(A_386,B_387),singleton(A_386)) = ordered_pair(A_386,B_387) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_15806,plain,
    ! [A_391] : ( unordered_pair(singleton(A_391),singleton(A_391)) = ordered_pair(A_391,A_391) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_15751]) ).

tff(c_15824,plain,
    ! [A_391] : ( singleton(singleton(A_391)) = ordered_pair(A_391,A_391) ),
    inference(superposition,[status(thm),theory(equality)],[c_15806,c_20]) ).

tff(c_2,plain,
    ! [B_2,A_1] : ( unordered_pair(B_2,A_1) = unordered_pair(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_15964,plain,
    ! [A_407,B_408] : ( unordered_pair(unordered_pair(A_407,B_408),singleton(B_408)) = ordered_pair(B_408,A_407) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_15751]) ).

tff(c_15784,plain,
    ! [A_1,B_2] : ( unordered_pair(unordered_pair(A_1,B_2),singleton(B_2)) = ordered_pair(B_2,A_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_15751]) ).

tff(c_18075,plain,
    ! [B_532,A_533] : ( unordered_pair(ordered_pair(B_532,A_533),singleton(singleton(B_532))) = ordered_pair(singleton(B_532),unordered_pair(A_533,B_532)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15964,c_15784]) ).

tff(c_18210,plain,
    ! [A_391,A_533] : ( unordered_pair(ordered_pair(A_391,A_533),ordered_pair(A_391,A_391)) = ordered_pair(singleton(A_391),unordered_pair(A_533,A_391)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15824,c_18075]) ).

tff(c_16,plain,
    ( ( '#skF_6' != '#skF_4' )
    | ( '#skF_5' != '#skF_3' ) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_28,plain,
    '#skF_5' != '#skF_3',
    inference(splitLeft,[status(thm)],[c_16]) ).

tff(c_18,plain,
    ordered_pair('#skF_5','#skF_6') = ordered_pair('#skF_3','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_121,plain,
    ! [A_41,B_42] : ( unordered_pair(unordered_pair(A_41,B_42),singleton(A_41)) = ordered_pair(A_41,B_42) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_154,plain,
    ! [A_41,B_42] : ( unordered_pair(singleton(A_41),unordered_pair(A_41,B_42)) = ordered_pair(A_41,B_42) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_121]) ).

tff(c_4,plain,
    ! [A_3,B_4] : ( unordered_pair(unordered_pair(A_3,B_4),singleton(A_3)) = ordered_pair(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_253,plain,
    ! [D_46,A_47,C_48,B_49] :
      ( ( D_46 = A_47 )
      | ( C_48 = A_47 )
      | ( unordered_pair(C_48,D_46) != unordered_pair(A_47,B_49) ) ),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_837,plain,
    ! [A_105,A_106,B_107,B_108] :
      ( ( singleton(A_105) = A_106 )
      | ( unordered_pair(A_105,B_107) = A_106 )
      | ( unordered_pair(A_106,B_108) != ordered_pair(A_105,B_107) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_253]) ).

tff(c_13318,plain,
    ! [A_357,A_356,B_358,B_359] :
      ( ( singleton(A_357) = singleton(A_356) )
      | ( unordered_pair(A_357,B_358) = singleton(A_356) )
      | ( ordered_pair(A_357,B_358) != ordered_pair(A_356,B_359) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_154,c_837]) ).

tff(c_13352,plain,
    ! [A_356,B_359] :
      ( ( singleton(A_356) = singleton('#skF_5') )
      | ( unordered_pair('#skF_5','#skF_6') = singleton(A_356) )
      | ( ordered_pair(A_356,B_359) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_13318]) ).

tff(c_13363,plain,
    ! [A_356,B_359] :
      ( ( singleton(A_356) = singleton('#skF_5') )
      | ( unordered_pair('#skF_6','#skF_5') = singleton(A_356) )
      | ( ordered_pair(A_356,B_359) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_13352]) ).

tff(c_14906,plain,
    ( ( singleton('#skF_5') = singleton('#skF_3') )
    | ( unordered_pair('#skF_6','#skF_5') = singleton('#skF_3') ) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_13363]) ).

tff(c_14928,plain,
    unordered_pair('#skF_6','#skF_5') = singleton('#skF_3'),
    inference(splitLeft,[status(thm)],[c_14906]) ).

tff(c_85,plain,
    ! [B_30,A_31,C_32] :
      ( ( B_30 = A_31 )
      | ( unordered_pair(B_30,C_32) != singleton(A_31) ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_91,plain,
    ! [B_2,A_31,A_1] :
      ( ( B_2 = A_31 )
      | ( unordered_pair(A_1,B_2) != singleton(A_31) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_85]) ).

tff(c_15088,plain,
    ! [A_31] :
      ( ( A_31 = '#skF_5' )
      | ( singleton(A_31) != singleton('#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_14928,c_91]) ).

tff(c_15116,plain,
    '#skF_5' = '#skF_3',
    inference(reflexivity,[status(thm),theory(equality)],[c_15088]) ).

tff(c_15118,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28,c_15116]) ).

tff(c_15119,plain,
    singleton('#skF_5') = singleton('#skF_3'),
    inference(splitRight,[status(thm)],[c_14906]) ).

tff(c_94,plain,
    ! [A_31,A_13] :
      ( ( A_31 = A_13 )
      | ( singleton(A_31) != singleton(A_13) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_85]) ).

tff(c_15329,plain,
    ! [A_31] :
      ( ( A_31 = '#skF_5' )
      | ( singleton(A_31) != singleton('#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15119,c_94]) ).

tff(c_15655,plain,
    '#skF_5' = '#skF_3',
    inference(reflexivity,[status(thm),theory(equality)],[c_15329]) ).

tff(c_15657,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28,c_15655]) ).

tff(c_15659,plain,
    '#skF_5' = '#skF_3',
    inference(splitRight,[status(thm)],[c_16]) ).

tff(c_15664,plain,
    ordered_pair('#skF_3','#skF_6') = ordered_pair('#skF_3','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_15659,c_18]) ).

tff(c_18219,plain,
    unordered_pair(ordered_pair('#skF_3','#skF_4'),singleton(singleton('#skF_3'))) = ordered_pair(singleton('#skF_3'),unordered_pair('#skF_6','#skF_3')),
    inference(superposition,[status(thm),theory(equality)],[c_15664,c_18075]) ).

tff(c_18230,plain,
    unordered_pair(ordered_pair('#skF_3','#skF_4'),ordered_pair('#skF_3','#skF_3')) = ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')),
    inference(demodulation,[status(thm),theory(equality)],[c_15824,c_2,c_18219]) ).

tff(c_23028,plain,
    ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')) = ordered_pair(singleton('#skF_3'),unordered_pair('#skF_4','#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_18210,c_18230]) ).

tff(c_26,plain,
    ! [C_21,B_20,A_19] :
      ( ( C_21 = B_20 )
      | ( unordered_pair(B_20,C_21) != singleton(A_19) ) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_16211,plain,
    ! [A_420,B_421,A_422] :
      ( ( unordered_pair(A_420,B_421) = singleton(A_420) )
      | ( singleton(A_422) != ordered_pair(A_420,B_421) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15751,c_26]) ).

tff(c_16216,plain,
    ! [A_422] :
      ( ( unordered_pair('#skF_3','#skF_6') = singleton('#skF_3') )
      | ( singleton(A_422) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15664,c_16211]) ).

tff(c_16222,plain,
    ! [A_423] : ( singleton(A_423) != ordered_pair('#skF_3','#skF_4') ),
    inference(splitLeft,[status(thm)],[c_16216]) ).

tff(c_16224,plain,
    ! [A_391] : ( ordered_pair(A_391,A_391) != ordered_pair('#skF_3','#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_15824,c_16222]) ).

tff(c_18323,plain,
    ! [A_19] :
      ( ( ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4') )
      | ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_18230,c_26]) ).

tff(c_18344,plain,
    ! [A_19] : ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_3','#skF_6')) ),
    inference(negUnitSimplification,[status(thm)],[c_16224,c_18323]) ).

tff(c_23222,plain,
    ! [A_19] : ( singleton(A_19) != ordered_pair(singleton('#skF_3'),unordered_pair('#skF_4','#skF_3')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_23028,c_18344]) ).

tff(c_15790,plain,
    ! [A_13] : ( unordered_pair(singleton(A_13),singleton(A_13)) = ordered_pair(A_13,A_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_15751]) ).

tff(c_16052,plain,
    ! [A_412,B_413] : ( unordered_pair(singleton(A_412),unordered_pair(A_412,B_413)) = ordered_pair(A_412,B_413) ),
    inference(superposition,[status(thm),theory(equality)],[c_15751,c_2]) ).

tff(c_16097,plain,
    ! [A_13] : ( unordered_pair(singleton(singleton(A_13)),ordered_pair(A_13,A_13)) = ordered_pair(singleton(A_13),singleton(A_13)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15790,c_16052]) ).

tff(c_16802,plain,
    ! [A_466] : ( unordered_pair(singleton(singleton(A_466)),ordered_pair(A_466,A_466)) = singleton(singleton(singleton(A_466))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_15824,c_16097]) ).

tff(c_16943,plain,
    ! [A_474] : ( unordered_pair(ordered_pair(A_474,A_474),ordered_pair(A_474,A_474)) = singleton(singleton(singleton(A_474))) ),
    inference(superposition,[status(thm),theory(equality)],[c_15824,c_16802]) ).

tff(c_17010,plain,
    ! [A_474] : ( singleton(singleton(singleton(A_474))) = singleton(ordered_pair(A_474,A_474)) ),
    inference(superposition,[status(thm),theory(equality)],[c_16943,c_20]) ).

tff(c_16121,plain,
    ! [B_415,A_416] : ( unordered_pair(singleton(B_415),unordered_pair(A_416,B_415)) = ordered_pair(B_415,A_416) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_16052]) ).

tff(c_18913,plain,
    ! [A_548,A_549] : ( unordered_pair(ordered_pair(A_548,A_548),unordered_pair(A_549,singleton(A_548))) = ordered_pair(singleton(A_548),A_549) ),
    inference(superposition,[status(thm),theory(equality)],[c_15824,c_16121]) ).

tff(c_19047,plain,
    ! [B_2,A_1] : ( unordered_pair(ordered_pair(B_2,B_2),ordered_pair(B_2,A_1)) = ordered_pair(singleton(B_2),unordered_pair(A_1,B_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15784,c_18913]) ).

tff(c_15658,plain,
    '#skF_6' != '#skF_4',
    inference(splitRight,[status(thm)],[c_16]) ).

tff(c_15893,plain,
    ! [D_394,A_395,C_396,B_397] :
      ( ( D_394 = A_395 )
      | ( C_396 = A_395 )
      | ( unordered_pair(C_396,D_394) != unordered_pair(A_395,B_397) ) ),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_16405,plain,
    ! [A_443,A_444,B_445,B_446] :
      ( ( singleton(A_443) = A_444 )
      | ( unordered_pair(A_443,B_445) = A_444 )
      | ( unordered_pair(A_444,B_446) != ordered_pair(A_443,B_445) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_15893]) ).

tff(c_16411,plain,
    ! [A_1,B_2,A_443,B_445] :
      ( ( unordered_pair(A_1,B_2) = singleton(A_443) )
      | ( unordered_pair(A_443,B_445) = unordered_pair(A_1,B_2) )
      | ( ordered_pair(B_2,A_1) != ordered_pair(A_443,B_445) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15784,c_16405]) ).

tff(c_56133,plain,
    ! [B_923,A_924,A_925,B_926] :
      ( ( ordered_pair(B_923,A_924) != ordered_pair(A_925,B_926) )
      | ( unordered_pair(A_924,B_923) = singleton(A_925) )
      | ( unordered_pair(A_925,B_926) != singleton(A_925) ) ),
    inference(factorization,[status(thm),theory(equality)],[c_16411]) ).

tff(c_56189,plain,
    ! [B_923,A_924] :
      ( ( ordered_pair(B_923,A_924) != ordered_pair('#skF_3','#skF_4') )
      | ( unordered_pair(A_924,B_923) = singleton('#skF_3') )
      | ( unordered_pair('#skF_3','#skF_6') != singleton('#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15664,c_56133]) ).

tff(c_57102,plain,
    unordered_pair('#skF_3','#skF_6') != singleton('#skF_3'),
    inference(splitLeft,[status(thm)],[c_56189]) ).

tff(c_16221,plain,
    ! [A_422] : ( singleton(A_422) != ordered_pair('#skF_3','#skF_4') ),
    inference(splitLeft,[status(thm)],[c_16216]) ).

tff(c_16511,plain,
    ! [A_459,B_460] : ( unordered_pair(ordered_pair(A_459,B_460),singleton(unordered_pair(A_459,B_460))) = ordered_pair(unordered_pair(A_459,B_460),singleton(A_459)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_15751]) ).

tff(c_16606,plain,
    unordered_pair(ordered_pair('#skF_3','#skF_4'),singleton(unordered_pair('#skF_3','#skF_6'))) = ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')),
    inference(superposition,[status(thm),theory(equality)],[c_15664,c_16511]) ).

tff(c_15902,plain,
    ! [A_3,A_395,B_4,B_397] :
      ( ( singleton(A_3) = A_395 )
      | ( unordered_pair(A_3,B_4) = A_395 )
      | ( unordered_pair(A_395,B_397) != ordered_pair(A_3,B_4) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_15893]) ).

tff(c_16632,plain,
    ! [A_3,B_4] :
      ( ( singleton(A_3) = ordered_pair('#skF_3','#skF_4') )
      | ( unordered_pair(A_3,B_4) = ordered_pair('#skF_3','#skF_4') )
      | ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(A_3,B_4) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_16606,c_15902]) ).

tff(c_16684,plain,
    ! [A_3,B_4] :
      ( ( unordered_pair(A_3,B_4) = ordered_pair('#skF_3','#skF_4') )
      | ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(A_3,B_4) ) ),
    inference(negUnitSimplification,[status(thm)],[c_16221,c_16632]) ).

tff(c_28315,plain,
    unordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair('#skF_3','#skF_4'),
    inference(reflexivity,[status(thm),theory(equality)],[c_16684]) ).

tff(c_16240,plain,
    ! [B_427,A_428,A_429,B_430] :
      ( ( B_427 = A_428 )
      | ( A_429 = A_428 )
      | ( unordered_pair(B_427,A_429) != unordered_pair(A_428,B_430) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_15893]) ).

tff(c_16255,plain,
    ! [A_1,B_2,A_428,B_430] :
      ( ( unordered_pair(A_1,B_2) = A_428 )
      | ( singleton(B_2) = A_428 )
      | ( unordered_pair(A_428,B_430) != ordered_pair(B_2,A_1) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15784,c_16240]) ).

tff(c_389649,plain,
    ! [A_2018,B_2019] :
      ( ( unordered_pair(A_2018,B_2019) = unordered_pair('#skF_3','#skF_6') )
      | ( unordered_pair('#skF_3','#skF_6') = singleton(B_2019) )
      | ( ordered_pair(B_2019,A_2018) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_28315,c_16255]) ).

tff(c_392990,plain,
    ! [A_2020,B_2021] :
      ( ( unordered_pair(ordered_pair('#skF_3','#skF_4'),singleton(unordered_pair(A_2020,B_2021))) = ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) )
      | ( unordered_pair('#skF_3','#skF_6') = singleton(B_2021) )
      | ( ordered_pair(B_2021,A_2020) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_389649,c_16606]) ).

tff(c_16603,plain,
    ! [B_2,A_1] : ( unordered_pair(ordered_pair(B_2,A_1),singleton(unordered_pair(A_1,B_2))) = ordered_pair(unordered_pair(B_2,A_1),singleton(B_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_16511]) ).

tff(c_393830,plain,
    ( ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair(unordered_pair('#skF_3','#skF_4'),singleton('#skF_3')) )
    | ( unordered_pair('#skF_3','#skF_6') = singleton('#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_392990,c_16603]) ).

tff(c_394828,plain,
    ( ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')) )
    | ( unordered_pair('#skF_3','#skF_6') = singleton('#skF_3') ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_393830]) ).

tff(c_394829,plain,
    ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) = ordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')),
    inference(negUnitSimplification,[status(thm)],[c_57102,c_394828]) ).

tff(c_16356,plain,
    ! [D_439,B_440,C_441,A_442] :
      ( ( D_439 = B_440 )
      | ( C_441 = B_440 )
      | ( unordered_pair(C_441,D_439) != unordered_pair(A_442,B_440) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_15893]) ).

tff(c_17843,plain,
    ! [B_520,D_521,C_522,A_523] :
      ( ( singleton(B_520) = D_521 )
      | ( singleton(B_520) = C_522 )
      | ( unordered_pair(C_522,D_521) != ordered_pair(B_520,A_523) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15784,c_16356]) ).

tff(c_17855,plain,
    ! [B_520,A_523] :
      ( ( singleton(unordered_pair('#skF_3','#skF_6')) = singleton(B_520) )
      | ( singleton(B_520) = ordered_pair('#skF_3','#skF_4') )
      | ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(B_520,A_523) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_16606,c_17843]) ).

tff(c_17886,plain,
    ! [B_520,A_523] :
      ( ( singleton(unordered_pair('#skF_3','#skF_6')) = singleton(B_520) )
      | ( ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')) != ordered_pair(B_520,A_523) ) ),
    inference(negUnitSimplification,[status(thm)],[c_16221,c_17855]) ).

tff(c_394965,plain,
    ! [B_520,A_523] :
      ( ( singleton(unordered_pair('#skF_3','#skF_6')) = singleton(B_520) )
      | ( ordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')) != ordered_pair(B_520,A_523) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394829,c_17886]) ).

tff(c_404068,plain,
    singleton(unordered_pair('#skF_3','#skF_6')) = singleton(unordered_pair('#skF_4','#skF_3')),
    inference(reflexivity,[status(thm),theory(equality)],[c_394965]) ).

tff(c_15725,plain,
    ! [B_378,A_379,C_380] :
      ( ( B_378 = A_379 )
      | ( unordered_pair(B_378,C_380) != singleton(A_379) ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_15734,plain,
    ! [A_379,A_13] :
      ( ( A_379 = A_13 )
      | ( singleton(A_379) != singleton(A_13) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_15725]) ).

tff(c_405552,plain,
    ! [A_379] :
      ( ( unordered_pair('#skF_3','#skF_6') = A_379 )
      | ( singleton(unordered_pair('#skF_4','#skF_3')) != singleton(A_379) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_404068,c_15734]) ).

tff(c_406419,plain,
    unordered_pair('#skF_3','#skF_6') = unordered_pair('#skF_4','#skF_3'),
    inference(reflexivity,[status(thm),theory(equality)],[c_405552]) ).

tff(c_15917,plain,
    ! [D_394,B_2,C_396,A_1] :
      ( ( D_394 = B_2 )
      | ( C_396 = B_2 )
      | ( unordered_pair(C_396,D_394) != unordered_pair(A_1,B_2) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_15893]) ).

tff(c_407217,plain,
    ! [D_394,C_396] :
      ( ( D_394 = '#skF_6' )
      | ( C_396 = '#skF_6' )
      | ( unordered_pair(C_396,D_394) != unordered_pair('#skF_4','#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_406419,c_15917]) ).

tff(c_419396,plain,
    ( ( '#skF_6' = '#skF_3' )
    | ( '#skF_6' = '#skF_4' ) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_407217]) ).

tff(c_419397,plain,
    '#skF_6' = '#skF_3',
    inference(negUnitSimplification,[status(thm)],[c_15658,c_419396]) ).

tff(c_407238,plain,
    unordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_6')) = ordered_pair('#skF_6','#skF_3'),
    inference(superposition,[status(thm),theory(equality)],[c_406419,c_15784]) ).

tff(c_419851,plain,
    unordered_pair(unordered_pair('#skF_4','#skF_3'),singleton('#skF_3')) = ordered_pair('#skF_3','#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_419397,c_419397,c_407238]) ).

tff(c_419865,plain,
    ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_15784,c_419851]) ).

tff(c_419867,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16224,c_419865]) ).

tff(c_419869,plain,
    unordered_pair('#skF_3','#skF_6') = singleton('#skF_3'),
    inference(splitRight,[status(thm)],[c_56189]) ).

tff(c_24764,plain,
    ! [A_643,B_644] : ( unordered_pair(singleton(unordered_pair(A_643,B_644)),ordered_pair(A_643,B_644)) = ordered_pair(unordered_pair(A_643,B_644),singleton(A_643)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_16052]) ).

tff(c_25027,plain,
    unordered_pair(singleton(unordered_pair('#skF_3','#skF_6')),ordered_pair('#skF_3','#skF_4')) = ordered_pair(unordered_pair('#skF_3','#skF_6'),singleton('#skF_3')),
    inference(superposition,[status(thm),theory(equality)],[c_15664,c_24764]) ).

tff(c_419905,plain,
    unordered_pair(singleton(singleton('#skF_3')),ordered_pair('#skF_3','#skF_4')) = ordered_pair(singleton('#skF_3'),singleton('#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_419869,c_419869,c_25027]) ).

tff(c_419948,plain,
    ordered_pair(singleton('#skF_3'),unordered_pair('#skF_4','#skF_3')) = singleton(ordered_pair('#skF_3','#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_17010,c_15824,c_19047,c_15824,c_419905]) ).

tff(c_419950,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_23222,c_419948]) ).

tff(c_419951,plain,
    unordered_pair('#skF_3','#skF_6') = singleton('#skF_3'),
    inference(splitRight,[status(thm)],[c_16216]) ).

tff(c_420039,plain,
    ! [A_19] :
      ( ( '#skF_6' = '#skF_3' )
      | ( singleton(A_19) != singleton('#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_419951,c_26]) ).

tff(c_420078,plain,
    ! [A_19] : ( singleton(A_19) != singleton('#skF_3') ),
    inference(splitLeft,[status(thm)],[c_420039]) ).

tff(c_420083,plain,
    $false,
    inference(reflexivity,[status(thm),theory(equality)],[c_420078]) ).

tff(c_420084,plain,
    '#skF_6' = '#skF_3',
    inference(splitRight,[status(thm)],[c_420039]) ).

tff(c_420087,plain,
    '#skF_3' != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_420084,c_15658]) ).

tff(c_15769,plain,
    ! [A_386,B_387] : ( unordered_pair(singleton(A_386),unordered_pair(A_386,B_387)) = ordered_pair(A_386,B_387) ),
    inference(superposition,[status(thm),theory(equality)],[c_15751,c_2]) ).

tff(c_420018,plain,
    unordered_pair(singleton('#skF_3'),singleton('#skF_3')) = ordered_pair('#skF_3','#skF_6'),
    inference(superposition,[status(thm),theory(equality)],[c_419951,c_15769]) ).

tff(c_420045,plain,
    ordered_pair('#skF_3','#skF_3') = ordered_pair('#skF_3','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_15664,c_15790,c_420018]) ).

tff(c_420290,plain,
    ! [A_2092,B_2093,A_2094] :
      ( ( unordered_pair(A_2092,B_2093) = singleton(B_2093) )
      | ( singleton(A_2094) != ordered_pair(B_2093,A_2092) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15964,c_26]) ).

tff(c_421266,plain,
    ! [A_2134,B_2135,A_2136] :
      ( ( unordered_pair(A_2134,B_2135) = singleton(B_2135) )
      | ( ordered_pair(B_2135,A_2134) != ordered_pair(A_2136,A_2136) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15824,c_420290]) ).

tff(c_421431,plain,
    ! [A_2139,B_2140] :
      ( ( unordered_pair(A_2139,B_2140) = singleton(B_2140) )
      | ( ordered_pair(B_2140,A_2139) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_420045,c_421266]) ).

tff(c_421525,plain,
    ! [B_2140,A_2139,A_19] :
      ( ( B_2140 = A_2139 )
      | ( singleton(B_2140) != singleton(A_19) )
      | ( ordered_pair(B_2140,A_2139) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_421431,c_26]) ).

tff(c_422229,plain,
    ! [A_2139,A_19] :
      ( ( A_2139 = A_19 )
      | ( ordered_pair(A_19,A_2139) != ordered_pair('#skF_3','#skF_4') ) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_421525]) ).

tff(c_422242,plain,
    '#skF_3' = '#skF_4',
    inference(reflexivity,[status(thm),theory(equality)],[c_422229]) ).

tff(c_422244,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_420087,c_422242]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU156+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/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
% 0.18/0.35  % Computer : n009.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit : 300
% 0.18/0.35  % WCLimit  : 300
% 0.18/0.35  % DateTime : Thu Aug  3 11:34:09 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 245.71/198.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 245.93/198.29  
% 245.93/198.29  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 245.93/198.33  
% 245.93/198.33  Inference rules
% 245.93/198.33  ----------------------
% 245.93/198.33  #Ref     : 129
% 245.93/198.33  #Sup     : 126084
% 245.93/198.33  #Fact    : 32
% 245.93/198.33  #Define  : 0
% 245.93/198.33  #Split   : 16
% 245.93/198.33  #Chain   : 0
% 245.93/198.33  #Close   : 0
% 245.93/198.33  
% 245.93/198.33  Ordering : KBO
% 245.93/198.33  
% 245.93/198.33  Simplification rules
% 245.93/198.33  ----------------------
% 245.93/198.33  #Subsume      : 20040
% 245.93/198.33  #Demod        : 88495
% 245.93/198.33  #Tautology    : 5250
% 245.93/198.33  #SimpNegUnit  : 5419
% 245.93/198.33  #BackRed      : 326
% 245.93/198.33  
% 245.93/198.33  #Partial instantiations: 0
% 245.93/198.33  #Strategies tried      : 1
% 245.93/198.33  
% 245.93/198.33  Timing (in seconds)
% 245.93/198.33  ----------------------
% 245.93/198.34  Preprocessing        : 0.49
% 245.93/198.34  Parsing              : 0.27
% 245.93/198.34  CNF conversion       : 0.03
% 245.93/198.34  Main loop            : 196.66
% 245.93/198.34  Inferencing          : 8.31
% 245.93/198.34  Reduction            : 77.93
% 245.93/198.34  Demodulation         : 69.45
% 245.93/198.34  BG Simplification    : 1.70
% 245.93/198.34  Subsumption          : 85.65
% 245.93/198.34  Abstraction          : 3.14
% 245.93/198.34  MUC search           : 0.00
% 245.93/198.34  Cooper               : 0.00
% 245.93/198.34  Total                : 197.27
% 245.93/198.34  Index Insertion      : 0.00
% 245.93/198.34  Index Deletion       : 0.00
% 245.93/198.34  Index Matching       : 0.00
% 245.93/198.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------