TSTP Solution File: SEV290^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV290^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n017.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 17:36:03 EDT 2022

% Result   : Theorem 25.21s 25.41s
% Output   : CNFRefutation 25.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   21 (  15 unt;   5 typ;   2 def)
%            Number of atoms       :   83 (  22 equ;   0 cnn)
%            Maximal formula atoms :    2 (   5 avg)
%            Number of connectives :  223 (  70   ~;  20   |;  19   &; 104   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  106 ( 106   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   53 (  19   ^  25   !;   9   ?;  53   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c0,type,
    c0: ( $i > $o ) > $o ).

thf(tp_cSUCC,type,
    cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).

thf(tp_c_less__eq_,type,
    c_less__eq_: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(tp_sK1_SY1,type,
    sK1_SY1: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).

thf(tp_sK2_SY20,type,
    sK2_SY20: ( ( ( $i > $o ) > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).

thf(cSUCC,definition,
    ( cSUCC
    = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
        ? [Xx: $i] :
          ( ( Xp @ Xx )
          & ( Xn
            @ ^ [Xt: $i] :
                ( ( Xt != Xx )
                & ( Xp @ Xt ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC) ).

thf(c_less__eq_,definition,
    ( c_less__eq_
    = ( ^ [Xx: ( $i > $o ) > $o,Xy: ( $i > $o ) > $o] :
        ! [Xp: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( Xp @ Xx )
            & ! [Xz: ( $i > $o ) > $o] :
                ( ( Xp @ Xz )
               => ( Xp @ ( cSUCC @ Xz ) ) ) )
         => ( Xp @ Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_less__eq_) ).

thf(1,conjecture,
    ? [A: ( ( $i > $o ) > $o ) > $o] :
    ! [Xx: ( $i > $o ) > $o] :
      ( ( A @ Xx )
     => ( c_less__eq_ @ Xx @ c0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE1) ).

thf(2,negated_conjecture,
    ( ( ? [A: ( ( $i > $o ) > $o ) > $o] :
        ! [Xx: ( $i > $o ) > $o] :
          ( ( A @ Xx )
         => ( c_less__eq_ @ Xx @ c0 ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ? [SY0: ( ( $i > $o ) > $o ) > $o] :
        ! [SY1: ( $i > $o ) > $o] :
          ( ( SY0 @ SY1 )
         => ! [SY8: ( ( $i > $o ) > $o ) > $o] :
              ( ( ( SY8 @ SY1 )
                & ! [SY4: ( $i > $o ) > $o] :
                    ( ( SY8 @ SY4 )
                   => ( SY8
                      @ ^ [SY5: $i > $o] :
                        ? [SY6: $i] :
                          ( ( SY5 @ SY6 )
                          & ( SY4
                            @ ^ [Xt: $i] :
                                ( ( Xt != SY6 )
                                & ( SY5 @ Xt ) ) ) ) ) ) )
             => ( SY8 @ c0 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,cSUCC,c_less__eq_]) ).

thf(4,plain,
    ( ( ~ ? [SY0: ( ( $i > $o ) > $o ) > $o] :
          ! [SY1: ( $i > $o ) > $o] :
            ( ( SY0 @ SY1 )
           => ! [SY8: ( ( $i > $o ) > $o ) > $o] :
                ( ( ( SY8 @ SY1 )
                  & ! [SY4: ( $i > $o ) > $o] :
                      ( ( SY8 @ SY4 )
                     => ( SY8
                        @ ^ [SY5: $i > $o] :
                          ? [SY6: $i] :
                            ( ( SY5 @ SY6 )
                            & ( SY4
                              @ ^ [Xt: $i] :
                                  ( ( Xt != SY6 )
                                  & ( SY5 @ Xt ) ) ) ) ) ) )
               => ( SY8 @ c0 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [SY0: ( ( $i > $o ) > $o ) > $o] :
          ( ( SY0 @ ( sK1_SY1 @ SY0 ) )
          & ! [SY25: ( $i > $o ) > $o] :
              ( ~ ( sK2_SY20 @ SY0 @ SY25 )
              | ( sK2_SY20 @ SY0
                @ ^ [SY5: $i > $o] :
                  ? [SY6: $i] :
                    ( ( SY5 @ SY6 )
                    & ( SY25
                      @ ^ [Xt: $i] :
                          ( ( Xt != SY6 )
                          & ( SY5 @ Xt ) ) ) ) ) )
          & ( sK2_SY20 @ SY0 @ ( sK1_SY1 @ SY0 ) )
          & ~ ( sK2_SY20 @ SY0 @ c0 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY0: ( ( $i > $o ) > $o ) > $o] :
          ( ( SY0 @ ( sK1_SY1 @ SY0 ) )
          & ! [SY25: ( $i > $o ) > $o] :
              ( ~ ( sK2_SY20 @ SY0 @ SY25 )
              | ( sK2_SY20 @ SY0
                @ ^ [SY5: $i > $o] :
                  ? [SY6: $i] :
                    ( ( SY5 @ SY6 )
                    & ( SY25
                      @ ^ [Xt: $i] :
                          ( ( Xt != SY6 )
                          & ( SY5 @ Xt ) ) ) ) ) )
          & ( sK2_SY20 @ SY0 @ ( sK1_SY1 @ SY0 ) )
          & ~ ( sK2_SY20 @ SY0 @ c0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [SX0: ( ( $i > $o ) > $o ) > $o] :
          ~ ( ~ ( SX0 @ ( sK1_SY1 @ SX0 ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX1: ( $i > $o ) > $o] :
                              ( ~ ( sK2_SY20 @ SX0 @ SX1 )
                              | ( sK2_SY20 @ SX0
                                @ ^ [SX2: $i > $o] :
                                    ~ ! [SX3: $i] :
                                        ~ ~ ( ~ ( SX2 @ SX3 )
                                            | ~ ( SX1
                                                @ ^ [SX4: $i] :
                                                    ~ ( ~ ( ( SX4 != SX3 ) )
                                                      | ~ ( SX2 @ SX4 ) ) ) ) ) )
                        | ~ ( sK2_SY20 @ SX0 @ ( sK1_SY1 @ SX0 ) ) )
                  | ~ ~ ( sK2_SY20 @ SX0 @ c0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6,cSUCC,c_less__eq_]) ).

thf(8,plain,
    ! [SV1: ( ( $i > $o ) > $o ) > $o] :
      ( ( ~ ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) )
            | ~ ~ ( ~ ~ ( ~ ! [SY29: ( $i > $o ) > $o] :
                              ( ~ ( sK2_SY20 @ SV1 @ SY29 )
                              | ( sK2_SY20 @ SV1
                                @ ^ [SX2: $i > $o] :
                                    ~ ! [SX3: $i] :
                                        ~ ~ ( ~ ( SX2 @ SX3 )
                                            | ~ ( SY29
                                                @ ^ [SX4: $i] :
                                                    ~ ( ~ ( ( SX4 != SX3 ) )
                                                      | ~ ( SX2 @ SX4 ) ) ) ) ) )
                        | ~ ( sK2_SY20 @ SV1 @ ( sK1_SY1 @ SV1 ) ) )
                  | ~ ~ ( sK2_SY20 @ SV1 @ c0 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7]) ).

thf(9,plain,
    ! [SV1: ( ( $i > $o ) > $o ) > $o] :
      ( ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) )
        | ~ ~ ( ~ ~ ( ~ ! [SY29: ( $i > $o ) > $o] :
                          ( ~ ( sK2_SY20 @ SV1 @ SY29 )
                          | ( sK2_SY20 @ SV1
                            @ ^ [SX2: $i > $o] :
                                ~ ! [SX3: $i] :
                                    ~ ~ ( ~ ( SX2 @ SX3 )
                                        | ~ ( SY29
                                            @ ^ [SX4: $i] :
                                                ~ ( ~ ( ( SX4 != SX3 ) )
                                                  | ~ ( SX2 @ SX4 ) ) ) ) ) )
                    | ~ ( sK2_SY20 @ SV1 @ ( sK1_SY1 @ SV1 ) ) )
              | ~ ~ ( sK2_SY20 @ SV1 @ c0 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[8]) ).

thf(10,plain,
    ! [SV1: ( ( $i > $o ) > $o ) > $o] :
      ( ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[9]) ).

thf(12,plain,
    ! [SV1: ( ( $i > $o ) > $o ) > $o] :
      ( ( SV1 @ ( sK1_SY1 @ SV1 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[10]) ).

thf(29,plain,
    $false = $true,
    inference(prim_subst,[status(thm)],[12:[bind(SV1,$thf( ^ [SV5: ( $i > $o ) > $o] : $false ))]]) ).

thf(48,plain,
    $false = $true,
    inference(sim,[status(thm)],[29]) ).

thf(49,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV290^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n017.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 13:47:29 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 454
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (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)..eprover: CPU time limit exceeded, terminating
% 25.21/25.40  .
% 25.21/25.41  
% 25.21/25.41  ********************************
% 25.21/25.41  *   All subproblems solved!    *
% 25.21/25.41  ********************************
% 25.21/25.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 25.21/25.41  
% 25.21/25.41  %**** Beginning of derivation protocol ****
% 25.21/25.41  % SZS output start CNFRefutation
% See solution above
% 25.21/25.41  
% 25.21/25.41  %**** End of derivation protocol ****
% 25.21/25.41  %**** no. of clauses in derivation: 14 ****
% 25.21/25.41  %**** clause counter: 48 ****
% 25.21/25.41  
% 25.21/25.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------