TSTP Solution File: SEU775^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU775^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n018.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  : 600s
% DateTime : Tue Jul 19 12:14:37 EDT 2022

% Result   : Theorem 76.05s 76.25s
% Output   : CNFRefutation 76.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   93 (  32 unt;  24 typ;   4 def)
%            Number of atoms       :  415 ( 183 equ;   0 cnn)
%            Maximal formula atoms :    4 (   6 avg)
%            Number of connectives :  917 (  50   ~;  57   |;   2   &; 802   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  126 ( 126   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;  10 con; 0-3 aty)
%            Number of variables   :  255 ( 197   ^  58   !;   0   ?; 255   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_breln,type,
    breln: $i > $i > $i > $o ).

thf(tp_breln1,type,
    breln1: $i > $i > $o ).

thf(tp_breln1invset,type,
    breln1invset: $i > $i > $i ).

thf(tp_cartprod,type,
    cartprod: $i > $i > $i ).

thf(tp_dpsetconstr,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(tp_in,type,
    in: $i > $i > $o ).

thf(tp_kpair,type,
    kpair: $i > $i > $i ).

thf(tp_sK10_E,type,
    sK10_E: ( $i > $i > $o ) > $i ).

thf(tp_sK11_E,type,
    sK11_E: ( $i > $i > $o ) > $i ).

thf(tp_sK12_E,type,
    sK12_E: $i ).

thf(tp_sK13_E,type,
    sK13_E: $i ).

thf(tp_sK14_E,type,
    sK14_E: $i ).

thf(tp_sK15_E,type,
    sK15_E: $i ).

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_SY450,type,
    sK2_SY450: $i ).

thf(tp_sK3_E,type,
    sK3_E: ( $i > $i > $o ) > $i ).

thf(tp_sK4_E,type,
    sK4_E: ( $i > $i > $o ) > $i ).

thf(tp_sK5_E,type,
    sK5_E: ( $i > $i > $o ) > $i ).

thf(tp_sK6_E,type,
    sK6_E: ( $i > $i > $o ) > $i ).

thf(tp_sK7_E,type,
    sK7_E: $i ).

thf(tp_sK8_E,type,
    sK8_E: ( $i > $i > $o ) > $i ).

thf(tp_sK9_E,type,
    sK9_E: ( $i > $i > $o ) > $i ).

thf(tp_setOfPairsIsBReln1,type,
    setOfPairsIsBReln1: $o ).

thf(tp_subset,type,
    subset: $i > $i > $o ).

thf(breln,definition,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).

thf(breln1,definition,
    ( breln1
    = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1) ).

thf(breln1invset,definition,
    ( breln1invset
    = ( ^ [A: $i,R: $i] :
          ( dpsetconstr @ A @ A
          @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invset) ).

thf(setOfPairsIsBReln1,definition,
    ( setOfPairsIsBReln1
    = ( ! [A: $i,Xphi: $i > $i > $o] :
          ( breln1 @ A
          @ ( dpsetconstr @ A @ A
            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).

thf(1,conjecture,
    ( setOfPairsIsBReln1
   => ! [A: $i,R: $i] :
        ( ( breln1 @ A @ R )
       => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invprop) ).

thf(2,negated_conjecture,
    ( ( setOfPairsIsBReln1
     => ! [A: $i,R: $i] :
          ( ( breln1 @ A @ R )
         => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    setOfPairsIsBReln1 = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [A: $i,R: $i] :
          ( ( breln1 @ A @ R )
         => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(5,plain,
    ( ( ~ ! [A: $i,R: $i] :
            ( ( breln1 @ A @ R )
           => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ( breln1 @ sK1_A @ sK2_SY450 )
      & ~ ( breln1 @ sK1_A @ ( breln1invset @ sK1_A @ sK2_SY450 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(7,plain,
    setOfPairsIsBReln1 = $true,
    inference(copy,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ( breln1 @ sK1_A @ sK2_SY450 )
      & ~ ( breln1 @ sK1_A @ ( breln1invset @ sK1_A @ sK2_SY450 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ~ ( ~ ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) )
          | ~ ~ ( subset
                @ ( dpsetconstr @ sK1_A @ sK1_A
                  @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
                @ ( cartprod @ sK1_A @ sK1_A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8,breln,breln1,breln1invset,setOfPairsIsBReln1]) ).

thf(10,plain,
    ( ( ! [SX0: $i,SX1: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ SX0 @ SX0
            @ ^ [SX2: $i,SX3: $i] : ( SX1 @ SX2 @ SX3 ) )
          @ ( cartprod @ SX0 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7,breln,breln1,breln1invset,setOfPairsIsBReln1]) ).

thf(11,plain,
    ( ( ~ ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) )
      | ~ ~ ( subset
            @ ( dpsetconstr @ sK1_A @ sK1_A
              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
            @ ( cartprod @ sK1_A @ sK1_A ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[9]) ).

thf(12,plain,
    ! [SV1: $i] :
      ( ( ! [SY451: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV1 @ SV1
              @ ^ [SX2: $i,SX3: $i] : ( SY451 @ SX2 @ SX3 ) )
            @ ( cartprod @ SV1 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ~ ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ~ ( subset
            @ ( dpsetconstr @ sK1_A @ sK1_A
              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
            @ ( cartprod @ sK1_A @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(15,plain,
    ! [SV2: $i > $i > $o,SV1: $i] :
      ( ( subset
        @ ( dpsetconstr @ SV1 @ SV1
          @ ^ [SY454: $i,SY455: $i] : ( SV2 @ SY454 @ SY455 ) )
        @ ( cartprod @ SV1 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(16,plain,
    ( ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ~ ( subset
          @ ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          @ ( cartprod @ sK1_A @ sK1_A ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(18,plain,
    ( ( subset
      @ ( dpsetconstr @ sK1_A @ sK1_A
        @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
      @ ( cartprod @ sK1_A @ sK1_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(19,plain,
    ! [SV3: $i > $i > $o,SV4: $i] :
      ( ( subset
        @ ( dpsetconstr @ SV4 @ SV4
          @ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) )
        @ ( cartprod @ SV4 @ SV4 ) )
      = $true ),
    inference(rename,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV3: $i > $i > $o,SV4: $i] :
      ( ( ( subset
          @ ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          @ ( cartprod @ sK1_A @ sK1_A ) )
        = ( subset
          @ ( dpsetconstr @ SV4 @ SV4
            @ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) )
          @ ( cartprod @ SV4 @ SV4 ) ) )
      = $false ),
    inference(res,[status(thm)],[18,19]) ).

thf(21,plain,
    ( ( ( subset
        @ ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
        @ ( cartprod @ sK1_A @ sK1_A ) )
      = ( subset @ sK2_SY450 @ ( cartprod @ sK1_A @ sK1_A ) ) )
    = $false ),
    inference(res,[status(thm)],[18,16]) ).

thf(22,plain,
    ( ( ( dpsetconstr @ sK1_A @ sK1_A
        @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
      = sK2_SY450 )
    = $false ),
    inference(extuni,[status(esa)],[21]) ).

thf(23,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK4_E @ SV3 ) @ ( sK3_E @ SV3 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV3 @ ( sK3_E @ SV3 ) @ ( sK4_E @ SV3 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_A ))]]) ).

thf(24,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK4_E @ SV3 ) @ ( sK3_E @ SV3 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV3 @ ( sK3_E @ SV3 ) @ ( sK4_E @ SV3 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_A ))]]) ).

thf(25,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
        = ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) ) )
      = $false ),
    inference(extuni,[status(esa)],[20:[bind(SV4,$thf( sK1_A ))]]) ).

thf(26,plain,
    ! [SV3: $i > $i > $o,SV4: $i] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( cartprod @ SV4 @ SV4 ) )
        = $false )
      | ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          = ( dpsetconstr @ SV4 @ SV4
            @ ^ [SX0: $i,SX1: $i] : ( SV3 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[20]) ).

thf(29,plain,
    ! [SV5: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK4_E @ SV5 ) @ ( sK3_E @ SV5 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
        = $true ) ),
    inference(rename,[status(thm)],[23]) ).

thf(35,plain,
    ( ( ( in
        @ ( kpair
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : $false )
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : $false ) )
        @ sK2_SY450 )
      = $true )
    | ( $false = $true ) ),
    inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SV9: $i] : ^ [SV10: $i] : $false ))]]) ).

thf(36,plain,
    ( ( in
      @ ( kpair
        @ ( sK4_E
          @ ^ [SX0: $i,SX1: $i] : $false )
        @ ( sK3_E
          @ ^ [SX0: $i,SX1: $i] : $false ) )
      @ sK2_SY450 )
    = $true ),
    inference(sim,[status(thm)],[35]) ).

thf(37,plain,
    ! [SV8: $i > $i > $o] :
      ( ( ( in
          @ ( kpair
            @ ( sK4_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV8 @ SX0 @ SX1 ) )
            @ ( sK3_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV8 @ SX0 @ SX1 ) ) )
          @ sK2_SY450 )
        = $true )
      | ( ( ~ ( SV8
              @ ( sK3_E
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV8 @ SX0 @ SX1 ) )
              @ ( sK4_E
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV8 @ SX0 @ SX1 ) ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SV6: $i] : ^ [SV7: $i] : ~ ( SV8 @ SV6 @ SV7 ) ))]]) ).

thf(38,plain,
    ( ( ( in
        @ ( kpair
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        @ sK2_SY450 )
      = $true )
    | ( ( ( ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
         != ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) ) )
      = $true ) ),
    inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SY464: $i] : ^ [SY465: $i] : ( SY464 != SY465 ) ))]]) ).

thf(39,plain,
    ( ( ( in
        @ ( kpair
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
        @ sK2_SY450 )
      = $true )
    | ( ( ( sK3_E
          @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
        = ( sK4_E
          @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
      = $true ) ),
    inference(prim_subst,[status(thm)],[29:[bind(SV5,$thf( ^ [SV14: $i] : ^ [SV13: $i] : ( SV14 = SV13 ) ))]]) ).

thf(41,plain,
    ! [SV8: $i > $i > $o] :
      ( ( ( SV8
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) )
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( in
          @ ( kpair
            @ ( sK4_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV8 @ SX0 @ SX1 ) )
            @ ( sK3_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV8 @ SX0 @ SX1 ) ) )
          @ sK2_SY450 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(42,plain,
    ( ( ( ( sK3_E
          @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
        = ( sK4_E
          @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
      = $false )
    | ( ( in
        @ ( kpair
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        @ sK2_SY450 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV63: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
        = $false ) ),
    inference(rename,[status(thm)],[24]) ).

thf(47,plain,
    ! [SV63: $i > $i > $o,SV5: $i > $i > $o] :
      ( ( ( ( in @ ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) @ sK2_SY450 )
          = ( in @ ( kpair @ ( sK4_E @ SV5 ) @ ( sK3_E @ SV5 ) ) @ sK2_SY450 ) )
        = $false )
      | ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
        = $false )
      | ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
        = $true ) ),
    inference(res,[status(thm)],[43,29]) ).

thf(52,plain,
    ( ( ( in
        @ ( kpair
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : $true )
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : $true ) )
        @ sK2_SY450 )
      = $false )
    | ( $true = $false ) ),
    inference(prim_subst,[status(thm)],[43:[bind(SV63,$thf( ^ [SV69: $i] : ^ [SV70: $i] : $true ))]]) ).

thf(53,plain,
    ( ( in
      @ ( kpair
        @ ( sK4_E
          @ ^ [SX0: $i,SX1: $i] : $true )
        @ ( sK3_E
          @ ^ [SX0: $i,SX1: $i] : $true ) )
      @ sK2_SY450 )
    = $false ),
    inference(sim,[status(thm)],[52]) ).

thf(55,plain,
    ! [SV66: $i > $i > $o] :
      ( ( ( in
          @ ( kpair
            @ ( sK4_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV66 @ SX0 @ SX1 ) )
            @ ( sK3_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV66 @ SX0 @ SX1 ) ) )
          @ sK2_SY450 )
        = $false )
      | ( ( ~ ( SV66
              @ ( sK3_E
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV66 @ SX0 @ SX1 ) )
              @ ( sK4_E
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV66 @ SX0 @ SX1 ) ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[43:[bind(SV63,$thf( ^ [SV64: $i] : ^ [SV65: $i] : ~ ( SV66 @ SV64 @ SV65 ) ))]]) ).

thf(56,plain,
    ( ( ( in
        @ ( kpair
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        @ sK2_SY450 )
      = $false )
    | ( ( ( ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
         != ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) ) )
      = $false ) ),
    inference(prim_subst,[status(thm)],[43:[bind(SV63,$thf( ^ [SY500: $i] : ^ [SY501: $i] : ( SY500 != SY501 ) ))]]) ).

thf(61,plain,
    ! [SV63: $i > $i > $o,SV5: $i > $i > $o] :
      ( ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
        = $true )
      | ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
        = $false )
      | ( ( ( sK3_E @ SV63 )
          = ( sK3_E @ SV5 ) )
        = $false )
      | ( ( ( sK4_E @ SV63 )
          = ( sK4_E @ SV5 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[47]) ).

thf(62,plain,
    ! [SV63: $i > $i > $o,SV5: $i > $i > $o] :
      ( ( ( SV5 @ ( sK3_E @ SV5 ) @ ( sK4_E @ SV5 ) )
        = $true )
      | ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
        = $false )
      | ( ( ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) )
          = ( kpair @ ( sK4_E @ SV5 ) @ ( sK3_E @ SV5 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[47]) ).

thf(63,plain,
    ! [SV66: $i > $i > $o] :
      ( ( ( SV66
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV66 @ SX0 @ SX1 ) )
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV66 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( in
          @ ( kpair
            @ ( sK4_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV66 @ SX0 @ SX1 ) )
            @ ( sK3_E
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV66 @ SX0 @ SX1 ) ) )
          @ sK2_SY450 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(64,plain,
    ( ( ( ( sK3_E
          @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
        = ( sK4_E
          @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
      = $true )
    | ( ( in
        @ ( kpair
          @ ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) )
          @ ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        @ sK2_SY450 )
      = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(65,plain,
    ! [SV127: $i > $i > $o] :
      ( ( ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
        = ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( SV127 @ SX0 @ SX1 ) ) )
      = $false ),
    inference(rename,[status(thm)],[25]) ).

thf(70,plain,
    ! [SV127: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK6_E @ SV127 ) @ ( sK5_E @ SV127 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV127 @ ( sK5_E @ SV127 ) @ ( sK6_E @ SV127 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[65]) ).

thf(71,plain,
    ! [SV127: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK6_E @ SV127 ) @ ( sK5_E @ SV127 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV127 @ ( sK5_E @ SV127 ) @ ( sK6_E @ SV127 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[65]) ).

thf(72,plain,
    ! [SV128: $i > $i > $o,SV129: $i] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( cartprod @ SV129 @ SV129 ) )
        = $false )
      | ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          = ( dpsetconstr @ SV129 @ SV129
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(rename,[status(thm)],[26]) ).

thf(81,plain,
    ! [SV128: $i > $i > $o,SV129: $i] :
      ( ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          = ( dpsetconstr @ SV129 @ SV129
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ( ( cartprod @ sK1_A @ sK1_A )
            = ( cartprod @ SV129 @ SV129 ) )
          = ( ( dpsetconstr @ sK1_A @ sK1_A
              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
            = ( dpsetconstr @ SV129 @ SV129
              @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[72]) ).

thf(82,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).

thf(83,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).

thf(85,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( cartprod @ sK1_A @ sK1_A ) )
        = $false )
      | ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).

thf(86,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).

thf(87,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).

thf(89,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( cartprod @ sK1_A @ sK1_A )
          = ( cartprod @ sK1_A @ sK1_A ) )
        = $false )
      | ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[81:[bind(SV129,$thf( sK1_A ))]]) ).

thf(90,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK11_E @ SV128 ) @ ( sK10_E @ SV128 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV128 @ ( sK10_E @ SV128 ) @ ( sK11_E @ SV128 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[72:[bind(SV129,$thf( sK1_A ))]]) ).

thf(91,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( in @ ( kpair @ ( sK11_E @ SV128 ) @ ( sK10_E @ SV128 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV128 @ ( sK10_E @ SV128 ) @ ( sK11_E @ SV128 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[72:[bind(SV129,$thf( sK1_A ))]]) ).

thf(92,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
        = ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
      = $false ),
    inference(extuni,[status(esa)],[72:[bind(SV129,$thf( sK1_A ))]]) ).

thf(93,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $false )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $false ) ),
    inference(sim,[status(thm)],[89]) ).

thf(94,plain,
    ! [SV128: $i > $i > $o] :
      ( ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY450 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( SV128 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK9_E @ SV128 ) @ ( sK8_E @ SV128 ) ) @ sK2_SY450 )
        = $true )
      | ( ( SV128 @ ( sK8_E @ SV128 ) @ ( sK9_E @ SV128 ) )
        = $true ) ),
    inference(sim,[status(thm)],[85]) ).

thf(99,plain,
    ! [SV63: $i > $i > $o] :
      ( ( ( ( in
            @ ( kpair
              @ ( sK4_E
                @ ^ [SX0: $i,SX1: $i] : $false )
              @ ( sK3_E
                @ ^ [SX0: $i,SX1: $i] : $false ) )
            @ sK2_SY450 )
          = ( in @ ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) @ sK2_SY450 ) )
        = $false )
      | ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
        = $false ) ),
    inference(res,[status(thm)],[36,43]) ).

thf(104,plain,
    ! [SV63: $i > $i > $o] :
      ( ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
        = $false )
      | ( ( ( sK3_E
            @ ^ [SX0: $i,SX1: $i] : $false )
          = ( sK3_E @ SV63 ) )
        = $false )
      | ( ( ( sK4_E
            @ ^ [SX0: $i,SX1: $i] : $false )
          = ( sK4_E @ SV63 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[99]) ).

thf(105,plain,
    ! [SV63: $i > $i > $o] :
      ( ( ( SV63 @ ( sK3_E @ SV63 ) @ ( sK4_E @ SV63 ) )
        = $false )
      | ( ( ( kpair
            @ ( sK4_E
              @ ^ [SX0: $i,SX1: $i] : $false )
            @ ( sK3_E
              @ ^ [SX0: $i,SX1: $i] : $false ) )
          = ( kpair @ ( sK4_E @ SV63 ) @ ( sK3_E @ SV63 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[99]) ).

thf(106,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[16,105,104,94,93,92,91,90,87,86,83,82,72,71,70,65,64,63,62,61,53,43,42,41,39,36,29,22,19,18]) ).

thf(107,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[106]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU775^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 03:24:05 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 722
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.40  
% 0.19/0.40   Prim_subst applied to clause 
% 0.19/0.40   
% 0.19/0.40  29:[ 0:<(in@((kpair@(sK4_E@SV5))@(sK3_E@SV5)))@sK2_SY35 = $true>-w(1)-i() 1:<(SV5@(sK3_E@SV5))@(sK4_E@SV5) = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 23)-o(DERIVED)-fv([ SV5 ])
% 1.16/1.35  .....
% 75.75/75.94  (rf:0,axioms:0,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 75.75/75.97  
% 75.75/75.97   Prim_subst applied to clause 
% 75.75/75.97   
% 75.75/75.97  29:[ 0:<(in@((kpair@(sK4_E@SV5))@(sK3_E@SV5)))@sK2_SY450 = $true>-w(1)-i() 1:<(SV5@(sK3_E@SV5))@(sK4_E@SV5) = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 23)-o(DERIVED)-fv([ SV5 ])
% 75.75/75.99  
% 75.75/75.99   Prim_subst applied to clause 
% 75.75/75.99   
% 75.75/75.99  43:[ 0:<(in@((kpair@(sK4_E@SV63))@(sK3_E@SV63)))@sK2_SY450 = $false>-w(1)-i() 1:<(SV63@(sK3_E@SV63))@(sK4_E@SV63) = $false>-w(1)-i() ]-mln(2)-w(2)-i(rename 24)-o(DERIVED)-fv([ SV63 ])
% 75.75/76.00  ..
% 76.05/76.25  
% 76.05/76.25  ********************************
% 76.05/76.25  *   All subproblems solved!    *
% 76.05/76.25  ********************************
% 76.05/76.25  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:10,foatp_calls:2,translation:fof_full)
% 76.07/76.26  
% 76.07/76.26  %**** Beginning of derivation protocol ****
% 76.07/76.26  % SZS output start CNFRefutation
% See solution above
% 76.07/76.26  
% 76.07/76.26  %**** End of derivation protocol ****
% 76.07/76.26  %**** no. of clauses in derivation: 65 ****
% 76.07/76.26  %**** clause counter: 106 ****
% 76.07/76.26  
% 76.07/76.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------