TSTP Solution File: SYO008^1 by LEO-II---1.7.0

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%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO008^1 : 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 : n022.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 : Thu Jul 21 17:31:20 EDT 2022

% Result   : Theorem 0.21s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   39 (  29 unt;   6 typ;   2 def)
%            Number of atoms       :   98 (  43 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  141 (  19   ~;   9   |;   2   &;  95   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  42   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   44 (   4   ^  40   !;   0   ?;  44   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_leibeq1,type,
    leibeq1: $i > $i > $o ).

thf(tp_leibeq2,type,
    leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).

thf(tp_sK1_SY0,type,
    sK1_SY0: $i > $i ).

thf(tp_sK2_SY14,type,
    sK2_SY14: $i > $i ).

thf(tp_sK3_SY20,type,
    sK3_SY20: ( $i > $i ) > $o ).

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

thf(leibeq1,definition,
    ( leibeq1
    = ( ^ [U: $i,V: $i] :
        ! [Q: $i > $o] :
          ( ( Q @ U )
         => ( Q @ V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq1) ).

thf(leibeq2,definition,
    ( leibeq2
    = ( ^ [X: $i > $i,Y: $i > $i] :
        ! [P: ( $i > $i ) > $o] :
          ( ( P @ X )
         => ( P @ Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq2) ).

thf(1,conjecture,
    ! [F: $i > $i,G: $i > $i] :
      ( ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) )
     => ( leibeq2 @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ( ( ! [F: $i > $i,G: $i > $i] :
          ( ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) )
         => ( leibeq2 @ F @ G ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [SY0: $i > $i,SY1: $i > $i] :
          ( ! [SY2: $i,SY5: $i > $o] :
              ( ( SY5 @ ( SY0 @ SY2 ) )
             => ( SY5 @ ( SY1 @ SY2 ) ) )
         => ! [SY8: ( $i > $i ) > $o] :
              ( ( SY8 @ SY0 )
             => ( SY8 @ SY1 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,leibeq1,leibeq2]) ).

thf(4,plain,
    ( ( ! [SY14: $i > $i] :
          ( ! [SY15: $i,SY16: $i > $o] :
              ( ( SY16 @ ( sK1_SY0 @ SY15 ) )
             => ( SY16 @ ( SY14 @ SY15 ) ) )
         => ! [SY17: ( $i > $i ) > $o] :
              ( ( SY17 @ sK1_SY0 )
             => ( SY17 @ SY14 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY18: $i,SY19: $i > $o] :
          ( ( SY19 @ ( sK1_SY0 @ SY18 ) )
         => ( SY19 @ ( sK2_SY14 @ SY18 ) ) )
     => ! [SY20: ( $i > $i ) > $o] :
          ( ( SY20 @ sK1_SY0 )
         => ( SY20 @ sK2_SY14 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY18: $i,SY19: $i > $o] :
          ( ( SY19 @ ( sK1_SY0 @ SY18 ) )
         => ( SY19 @ ( sK2_SY14 @ SY18 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SY20: ( $i > $i ) > $o] :
          ( ( SY20 @ sK1_SY0 )
         => ( SY20 @ sK2_SY14 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ~ ! [SY20: ( $i > $i ) > $o] :
            ( ( SY20 @ sK1_SY0 )
           => ( SY20 @ sK2_SY14 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ( sK3_SY20 @ sK1_SY0 )
      & ~ ( sK3_SY20 @ sK2_SY14 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [SY18: $i,SY19: $i > $o] :
          ( ~ ( SY19 @ ( sK1_SY0 @ SY18 ) )
          | ( SY19 @ ( sK2_SY14 @ SY18 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ! [SY18: $i,SY19: $i > $o] :
          ( ~ ( SY19 @ ( sK1_SY0 @ SY18 ) )
          | ( SY19 @ ( sK2_SY14 @ SY18 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ( sK3_SY20 @ sK1_SY0 )
      & ~ ( sK3_SY20 @ sK2_SY14 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ~ ( ~ ( sK3_SY20 @ sK1_SY0 )
          | ~ ~ ( sK3_SY20 @ sK2_SY14 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12,leibeq1,leibeq2]) ).

thf(14,plain,
    ! [SV1: $i] :
      ( ( ! [SY21: $i > $o] :
            ( ~ ( SY21 @ ( sK1_SY0 @ SV1 ) )
            | ( SY21 @ ( sK2_SY14 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ~ ( sK3_SY20 @ sK1_SY0 )
      | ~ ~ ( sK3_SY20 @ sK2_SY14 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV1: $i,SV2: $i > $o] :
      ( ( ~ ( SV2 @ ( sK1_SY0 @ SV1 ) )
        | ( SV2 @ ( sK2_SY14 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ( sK3_SY20 @ sK1_SY0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ~ ( sK3_SY20 @ sK2_SY14 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV1: $i,SV2: $i > $o] :
      ( ( ( ~ ( SV2 @ ( sK1_SY0 @ SV1 ) ) )
        = $true )
      | ( ( SV2 @ ( sK2_SY14 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(20,plain,
    ( ( sK3_SY20 @ sK1_SY0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ( sK3_SY20 @ sK2_SY14 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV1: $i,SV2: $i > $o] :
      ( ( ( SV2 @ ( sK1_SY0 @ SV1 ) )
        = $false )
      | ( ( SV2 @ ( sK2_SY14 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
    ( ( sK3_SY20 @ sK2_SY14 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(24,plain,
    ! [SV1: $i] :
      ( ( ( ( sK1_SY0 @ SV1 )
          = ( sK1_SY0 @ SV1 ) )
        = $false )
      | ( ( ( sK2_SY14 @ SV1 )
          = ( sK1_SY0 @ SV1 ) )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[22:[bind(SV2,$thf( ^ [SV3: $i] : ( SV3 = ( sK1_SY0 @ SV1 ) ) ))]]) ).

thf(25,plain,
    ! [SV1: $i] :
      ( ( ( sK2_SY14 @ SV1 )
        = ( sK1_SY0 @ SV1 ) )
      = $true ),
    inference(sim,[status(thm)],[24]) ).

thf(26,plain,
    ( ( ( sK3_SY20 @ sK2_SY14 )
      = ( sK3_SY20 @ sK1_SY0 ) )
    = $false ),
    inference(res,[status(thm)],[23,20]) ).

thf(27,plain,
    ( ( ( sK2_SY14 @ sK4_E )
      = ( sK1_SY0 @ sK4_E ) )
    = $false ),
    inference(extuni,[status(esa)],[26]) ).

thf(28,plain,
    ! [SV4: $i] :
      ( ( ( sK2_SY14 @ SV4 )
        = ( sK1_SY0 @ SV4 ) )
      = $true ),
    inference(rename,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV4: $i] :
      ( ( ( ( sK2_SY14 @ sK4_E )
          = ( sK1_SY0 @ sK4_E ) )
        = ( ( sK2_SY14 @ SV4 )
          = ( sK1_SY0 @ SV4 ) ) )
      = $false ),
    inference(res,[status(thm)],[27,28]) ).

thf(33,plain,
    $false = $true,
    inference(extuni,[status(esa)],[30:[bind(SV4,$thf( sK4_E ))]]) ).

thf(34,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO008^1 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n022.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 : Fri Jul  8 17:15:26 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: 321
% 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).
% 0.21/0.40  
% 0.21/0.40  ********************************
% 0.21/0.40  *   All subproblems solved!    *
% 0.21/0.40  ********************************
% 0.21/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:33,loop_count:4,foatp_calls:2,translation:fof_full)
% 0.21/0.40  
% 0.21/0.40  %**** Beginning of derivation protocol ****
% 0.21/0.40  % SZS output start CNFRefutation
% See solution above
% 0.21/0.40  
% 0.21/0.40  %**** End of derivation protocol ****
% 0.21/0.40  %**** no. of clauses in derivation: 31 ****
% 0.21/0.40  %**** clause counter: 33 ****
% 0.21/0.40  
% 0.21/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:33,loop_count:4,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------