TSTP Solution File: GRP205-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP205-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n021.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 10:16:57 EDT 2022

% Result   : Unsatisfiable 11.36s 11.58s
% Output   : CNFRefutation 11.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   64 (  55 unt;   9 typ;   0 def)
%            Number of atoms       :  141 (  90 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  258 (   6   ~;   0   |;   0   &; 252   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   74 (   0   ^  74   !;   0   ?;  74   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_identity,type,
    identity: $i ).

thf(tp_left_division,type,
    left_division: $i > $i > $i ).

thf(tp_left_inverse,type,
    left_inverse: $i > $i ).

thf(tp_multiply,type,
    multiply: $i > $i > $i ).

thf(tp_right_division,type,
    right_division: $i > $i > $i ).

thf(tp_right_inverse,type,
    right_inverse: $i > $i ).

thf(tp_x,type,
    x: $i ).

thf(tp_y,type,
    y: $i ).

thf(tp_z,type,
    z: $i ).

thf(1,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( multiply @ ( multiply @ ( multiply @ X @ Y ) @ X ) @ Z )
      = ( multiply @ X @ ( multiply @ Y @ ( multiply @ X @ Z ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',moufang3) ).

thf(2,axiom,
    ! [X: $i] :
      ( ( multiply @ ( left_inverse @ X ) @ X )
      = identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

thf(3,axiom,
    ! [X: $i] :
      ( ( multiply @ X @ ( right_inverse @ X ) )
      = identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ( right_division @ ( multiply @ X @ Y ) @ Y )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_division_multiply) ).

thf(5,axiom,
    ! [X: $i,Y: $i] :
      ( ( multiply @ ( right_division @ X @ Y ) @ Y )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_right_division) ).

thf(6,axiom,
    ! [X: $i,Y: $i] :
      ( ( left_division @ X @ ( multiply @ X @ Y ) )
      = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_division_multiply) ).

thf(7,axiom,
    ! [X: $i,Y: $i] :
      ( ( multiply @ X @ ( left_division @ X @ Y ) )
      = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_left_division) ).

thf(8,axiom,
    ! [X: $i] :
      ( ( multiply @ X @ identity )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).

thf(9,axiom,
    ! [X: $i] :
      ( ( multiply @ identity @ X )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

thf(10,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(11,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[10]) ).

thf(12,negated_conjecture,
    ( multiply @ x @ ( multiply @ ( multiply @ y @ z ) @ x ) )
 != ( multiply @ ( multiply @ x @ y ) @ ( multiply @ z @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang4) ).

thf(13,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ ( multiply @ ( multiply @ X @ Y ) @ X ) @ Z )
          = ( multiply @ X @ ( multiply @ Y @ ( multiply @ X @ Z ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ ( left_inverse @ X ) @ X )
          = identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ X @ ( right_inverse @ X ) )
          = identity ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( right_division @ ( multiply @ X @ Y ) @ Y )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( multiply @ ( right_division @ X @ Y ) @ Y )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( left_division @ X @ ( multiply @ X @ Y ) )
          = Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( multiply @ X @ ( left_division @ X @ Y ) )
          = Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ X @ identity )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(22,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ identity @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(23,plain,
    ( ( ( ( multiply @ x @ ( multiply @ ( multiply @ y @ z ) @ x ) )
       != ( multiply @ ( multiply @ x @ y ) @ ( multiply @ z @ x ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(24,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(25,plain,
    ( ( ( ( multiply @ x @ ( multiply @ ( multiply @ y @ z ) @ x ) )
       != ( multiply @ ( multiply @ x @ y ) @ ( multiply @ z @ x ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(26,plain,
    ( ( ( ( multiply @ x @ ( multiply @ ( multiply @ y @ z ) @ x ) )
       != ( multiply @ ( multiply @ x @ y ) @ ( multiply @ z @ x ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(27,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ identity @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(28,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ X @ identity )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( multiply @ X @ ( left_division @ X @ Y ) )
          = Y ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( left_division @ X @ ( multiply @ X @ Y ) )
          = Y ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(31,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( multiply @ ( right_division @ X @ Y ) @ Y )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(32,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( right_division @ ( multiply @ X @ Y ) @ Y )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(33,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ X @ ( right_inverse @ X ) )
          = identity ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(34,plain,
    ( ( ! [X: $i] :
          ( ( multiply @ ( left_inverse @ X ) @ X )
          = identity ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(35,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( multiply @ ( multiply @ ( multiply @ X @ Y ) @ X ) @ Z )
          = ( multiply @ X @ ( multiply @ Y @ ( multiply @ X @ Z ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(36,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(37,plain,
    ( ( ( multiply @ x @ ( multiply @ ( multiply @ y @ z ) @ x ) )
      = ( multiply @ ( multiply @ x @ y ) @ ( multiply @ z @ x ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(38,plain,
    ! [SV1: $i] :
      ( ( ( multiply @ identity @ SV1 )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(39,plain,
    ! [SV2: $i] :
      ( ( ( multiply @ SV2 @ identity )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(40,plain,
    ! [SV3: $i] :
      ( ( ! [SY15: $i] :
            ( ( multiply @ SV3 @ ( left_division @ SV3 @ SY15 ) )
            = SY15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(41,plain,
    ! [SV4: $i] :
      ( ( ! [SY16: $i] :
            ( ( left_division @ SV4 @ ( multiply @ SV4 @ SY16 ) )
            = SY16 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(42,plain,
    ! [SV5: $i] :
      ( ( ! [SY17: $i] :
            ( ( multiply @ ( right_division @ SV5 @ SY17 ) @ SY17 )
            = SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(43,plain,
    ! [SV6: $i] :
      ( ( ! [SY18: $i] :
            ( ( right_division @ ( multiply @ SV6 @ SY18 ) @ SY18 )
            = SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(44,plain,
    ! [SV7: $i] :
      ( ( ( multiply @ SV7 @ ( right_inverse @ SV7 ) )
        = identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(45,plain,
    ! [SV8: $i] :
      ( ( ( multiply @ ( left_inverse @ SV8 ) @ SV8 )
        = identity )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(46,plain,
    ! [SV9: $i] :
      ( ( ! [SY19: $i,SY20: $i] :
            ( ( multiply @ ( multiply @ ( multiply @ SV9 @ SY19 ) @ SV9 ) @ SY20 )
            = ( multiply @ SV9 @ ( multiply @ SY19 @ ( multiply @ SV9 @ SY20 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(47,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(48,plain,
    ! [SV10: $i,SV3: $i] :
      ( ( ( multiply @ SV3 @ ( left_division @ SV3 @ SV10 ) )
        = SV10 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(49,plain,
    ! [SV11: $i,SV4: $i] :
      ( ( ( left_division @ SV4 @ ( multiply @ SV4 @ SV11 ) )
        = SV11 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(50,plain,
    ! [SV12: $i,SV5: $i] :
      ( ( ( multiply @ ( right_division @ SV5 @ SV12 ) @ SV12 )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(51,plain,
    ! [SV13: $i,SV6: $i] :
      ( ( ( right_division @ ( multiply @ SV6 @ SV13 ) @ SV13 )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(52,plain,
    ! [SV14: $i,SV9: $i] :
      ( ( ! [SY21: $i] :
            ( ( multiply @ ( multiply @ ( multiply @ SV9 @ SV14 ) @ SV9 ) @ SY21 )
            = ( multiply @ SV9 @ ( multiply @ SV14 @ ( multiply @ SV9 @ SY21 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(53,plain,
    ! [SV15: $i,SV14: $i,SV9: $i] :
      ( ( ( multiply @ ( multiply @ ( multiply @ SV9 @ SV14 ) @ SV9 ) @ SV15 )
        = ( multiply @ SV9 @ ( multiply @ SV14 @ ( multiply @ SV9 @ SV15 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(54,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[37,53,51,50,49,48,47,45,44,39,38]) ).

thf(55,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP205-1 : TPTP v8.1.0. Released v2.3.0.
% 0.11/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 03:36:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 10
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:10,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:12,loop_count:0,foatp_calls:0,translation:fof_full)..
% 11.36/11.58  
% 11.36/11.58  ********************************
% 11.36/11.58  *   All subproblems solved!    *
% 11.36/11.58  ********************************
% 11.36/11.58  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:54,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.36/11.58  
% 11.36/11.58  %**** Beginning of derivation protocol ****
% 11.36/11.58  % SZS output start CNFRefutation
% See solution above
% 11.36/11.58  
% 11.36/11.58  %**** End of derivation protocol ****
% 11.36/11.58  %**** no. of clauses in derivation: 55 ****
% 11.36/11.58  %**** clause counter: 54 ****
% 11.36/11.58  
% 11.36/11.58  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:54,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------