TSTP Solution File: GRP710-10 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP710-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n019.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 : Sat Jul 16 10:19:42 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   41 (  36 unt;   5 typ;   0 def)
%            Number of atoms       :   92 (  56 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  131 (   7   ~;   0   |;   0   &; 124   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   40 (   0   ^  40   !;   0   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_i,type,
    i: $i > $i ).

thf(tp_mult,type,
    mult: $i > $i > $i ).

thf(tp_unit,type,
    unit: $i ).

thf(tp_x0,type,
    x0: $i ).

thf(tp_x1,type,
    x1: $i ).

thf(1,axiom,
    ! [A: $i] :
      ( ( mult @ ( i @ A ) @ A )
      = unit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( mult @ A @ ( i @ A ) )
      = unit ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
      = ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).

thf(6,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(7,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,negated_conjecture,
    ! [X2: $i] :
      ( ( mult @ x0 @ X2 )
     != x1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).

thf(9,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [A: $i] :
          ( ( mult @ ( i @ A ) @ A )
          = unit ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(11,plain,
    ( ( ! [A: $i] :
          ( ( mult @ A @ ( i @ A ) )
          = unit ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(12,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
          = ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(13,plain,
    ( ( ! [A: $i] :
          ( ( mult @ unit @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(14,plain,
    ( ( ! [A: $i] :
          ( ( mult @ A @ unit )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(15,plain,
    ( ( ! [X2: $i] :
          ( ( mult @ x0 @ X2 )
         != x1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(16,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(17,plain,
    ( ( ! [X2: $i] :
          ( ( mult @ x0 @ X2 )
         != x1 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(18,plain,
    ( ( ! [X2: $i] :
          ( ( mult @ x0 @ X2 )
         != x1 ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(19,plain,
    ( ( ! [A: $i] :
          ( ( mult @ A @ unit )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(20,plain,
    ( ( ! [A: $i] :
          ( ( mult @ unit @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(21,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
          = ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(22,plain,
    ( ( ! [A: $i] :
          ( ( mult @ A @ ( i @ A ) )
          = unit ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(23,plain,
    ( ( ! [A: $i] :
          ( ( mult @ ( i @ A ) @ A )
          = unit ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(24,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(25,plain,
    ! [SV1: $i] :
      ( ( ( ( mult @ x0 @ SV1 )
         != x1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(26,plain,
    ! [SV2: $i] :
      ( ( ( mult @ SV2 @ unit )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(27,plain,
    ! [SV3: $i] :
      ( ( ( mult @ unit @ SV3 )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(28,plain,
    ! [SV4: $i] :
      ( ( ! [SY8: $i,SY9: $i] :
            ( ( mult @ SV4 @ ( mult @ SY8 @ ( mult @ SY8 @ SY9 ) ) )
            = ( mult @ ( mult @ ( mult @ SV4 @ SY8 ) @ SY8 ) @ SY9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(29,plain,
    ! [SV5: $i] :
      ( ( ( mult @ SV5 @ ( i @ SV5 ) )
        = unit )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(30,plain,
    ! [SV6: $i] :
      ( ( ( mult @ ( i @ SV6 ) @ SV6 )
        = unit )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(31,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(32,plain,
    ! [SV1: $i] :
      ( ( ( mult @ x0 @ SV1 )
        = x1 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(33,plain,
    ! [SV7: $i,SV4: $i] :
      ( ( ! [SY10: $i] :
            ( ( mult @ SV4 @ ( mult @ SV7 @ ( mult @ SV7 @ SY10 ) ) )
            = ( mult @ ( mult @ ( mult @ SV4 @ SV7 ) @ SV7 ) @ SY10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(34,plain,
    ! [SV8: $i,SV7: $i,SV4: $i] :
      ( ( ( mult @ SV4 @ ( mult @ SV7 @ ( mult @ SV7 @ SV8 ) ) )
        = ( mult @ ( mult @ ( mult @ SV4 @ SV7 ) @ SV7 ) @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(35,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[26,34,32,31,30,29,27]) ).

thf(36,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP710-10 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jun 14 12:59:54 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.34  
% 0.19/0.34   No.of.Axioms: 6
% 0.19/0.34  
% 0.19/0.34   Length.of.Defs: 0
% 0.19/0.34  
% 0.19/0.34   Contains.Choice.Funs: false
% 0.19/0.34  (rf:0,axioms:6,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.19/0.40  
% 0.19/0.40  ********************************
% 0.19/0.40  *   All subproblems solved!    *
% 0.19/0.40  ********************************
% 0.19/0.40  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40  
% 0.19/0.40  %**** Beginning of derivation protocol ****
% 0.19/0.40  % SZS output start CNFRefutation
% See solution above
% 0.19/0.40  
% 0.19/0.40  %**** End of derivation protocol ****
% 0.19/0.40  %**** no. of clauses in derivation: 36 ****
% 0.19/0.40  %**** clause counter: 35 ****
% 0.19/0.40  
% 0.19/0.40  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------