TSTP Solution File: GRP660+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP660+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n023.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 10:19:22 EDT 2022

% Result   : Theorem 4.90s 5.16s
% Output   : CNFRefutation 4.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   43 (  34 unt;   5 typ;   0 def)
%            Number of atoms       :  116 (  80 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  236 (  10   ~;   6   |;   4   &; 216   @)
%                                         (   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     :    8 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   72 (   0   ^  68   !;   4   ?;  72   :)

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

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

thf(tp_rd,type,
    rd: $i > $i > $i ).

thf(tp_sK1_X1,type,
    sK1_X1: $i > $i ).

thf(tp_sK2_X1,type,
    sK2_X1: $i > $i ).

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

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

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

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

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

thf(6,conjecture,
    ? [X0: $i] :
    ! [X1: $i] :
      ( ( ( mult @ X1 @ X0 )
        = X1 )
      & ( ( mult @ X0 @ X1 )
        = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

thf(7,negated_conjecture,
    ( ( ? [X0: $i] :
        ! [X1: $i] :
          ( ( ( mult @ X1 @ X0 )
            = X1 )
          & ( ( mult @ X0 @ X1 )
            = X1 ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,plain,
    ( ( ? [X0: $i] :
        ! [X1: $i] :
          ( ( ( mult @ X1 @ X0 )
            = X1 )
          & ( ( mult @ X0 @ X1 )
            = X1 ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A )
          = ( mult @ A @ ( mult @ B @ ( mult @ C @ A ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( rd @ ( mult @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(11,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( mult @ ( rd @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(12,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( ld @ A @ ( mult @ A @ B ) )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( mult @ A @ ( ld @ A @ B ) )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(14,plain,
    ( ( ~ ? [X0: $i] :
          ! [X1: $i] :
            ( ( ( mult @ X1 @ X0 )
              = X1 )
            & ( ( mult @ X0 @ X1 )
              = X1 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(15,plain,
    ( ( ! [X0: $i] :
          ( ( ( mult @ ( sK2_X1 @ X0 ) @ X0 )
           != ( sK2_X1 @ X0 ) )
          | ( ( mult @ X0 @ ( sK1_X1 @ X0 ) )
           != ( sK1_X1 @ X0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[14]) ).

thf(16,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( mult @ A @ ( ld @ A @ B ) )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( ld @ A @ ( mult @ A @ B ) )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(18,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( mult @ ( rd @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(19,plain,
    ( ( ! [B: $i,A: $i] :
          ( ( rd @ ( mult @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(20,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A )
          = ( mult @ A @ ( mult @ B @ ( mult @ C @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(21,plain,
    ( ( ! [X0: $i] :
          ( ( ( mult @ ( sK2_X1 @ X0 ) @ X0 )
           != ( sK2_X1 @ X0 ) )
          | ( ( mult @ X0 @ ( sK1_X1 @ X0 ) )
           != ( sK1_X1 @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(22,plain,
    ! [SV1: $i] :
      ( ( ! [SY13: $i] :
            ( ( mult @ SY13 @ ( ld @ SY13 @ SV1 ) )
            = SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(23,plain,
    ! [SV2: $i] :
      ( ( ! [SY14: $i] :
            ( ( ld @ SY14 @ ( mult @ SY14 @ SV2 ) )
            = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(24,plain,
    ! [SV3: $i] :
      ( ( ! [SY15: $i] :
            ( ( mult @ ( rd @ SY15 @ SV3 ) @ SV3 )
            = SY15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(25,plain,
    ! [SV4: $i] :
      ( ( ! [SY16: $i] :
            ( ( rd @ ( mult @ SY16 @ SV4 ) @ SV4 )
            = SY16 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(26,plain,
    ! [SV5: $i] :
      ( ( ! [SY17: $i,SY18: $i] :
            ( ( mult @ ( mult @ ( mult @ SY18 @ SY17 ) @ SV5 ) @ SY18 )
            = ( mult @ SY18 @ ( mult @ SY17 @ ( mult @ SV5 @ SY18 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(27,plain,
    ! [SV6: $i] :
      ( ( ( ( mult @ ( sK2_X1 @ SV6 ) @ SV6 )
         != ( sK2_X1 @ SV6 ) )
        | ( ( mult @ SV6 @ ( sK1_X1 @ SV6 ) )
         != ( sK1_X1 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(28,plain,
    ! [SV1: $i,SV7: $i] :
      ( ( ( mult @ SV7 @ ( ld @ SV7 @ SV1 ) )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(29,plain,
    ! [SV2: $i,SV8: $i] :
      ( ( ( ld @ SV8 @ ( mult @ SV8 @ SV2 ) )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(30,plain,
    ! [SV3: $i,SV9: $i] :
      ( ( ( mult @ ( rd @ SV9 @ SV3 ) @ SV3 )
        = SV9 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(31,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( rd @ ( mult @ SV10 @ SV4 ) @ SV4 )
        = SV10 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(32,plain,
    ! [SV5: $i,SV11: $i] :
      ( ( ! [SY19: $i] :
            ( ( mult @ ( mult @ ( mult @ SY19 @ SV11 ) @ SV5 ) @ SY19 )
            = ( mult @ SY19 @ ( mult @ SV11 @ ( mult @ SV5 @ SY19 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(33,plain,
    ! [SV6: $i] :
      ( ( ( ( ( mult @ ( sK2_X1 @ SV6 ) @ SV6 )
           != ( sK2_X1 @ SV6 ) ) )
        = $true )
      | ( ( ( ( mult @ SV6 @ ( sK1_X1 @ SV6 ) )
           != ( sK1_X1 @ SV6 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(34,plain,
    ! [SV5: $i,SV11: $i,SV12: $i] :
      ( ( ( mult @ ( mult @ ( mult @ SV12 @ SV11 ) @ SV5 ) @ SV12 )
        = ( mult @ SV12 @ ( mult @ SV11 @ ( mult @ SV5 @ SV12 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV6: $i] :
      ( ( ( ( mult @ ( sK2_X1 @ SV6 ) @ SV6 )
          = ( sK2_X1 @ SV6 ) )
        = $false )
      | ( ( ( ( mult @ SV6 @ ( sK1_X1 @ SV6 ) )
           != ( sK1_X1 @ SV6 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(36,plain,
    ! [SV6: $i] :
      ( ( ( ( mult @ SV6 @ ( sK1_X1 @ SV6 ) )
          = ( sK1_X1 @ SV6 ) )
        = $false )
      | ( ( ( mult @ ( sK2_X1 @ SV6 ) @ SV6 )
          = ( sK2_X1 @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(37,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[28,36,34,31,30,29]) ).

thf(38,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP660+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n023.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 13 19:27:21 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 5
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full)..
% 4.90/5.16  
% 4.90/5.16  ********************************
% 4.90/5.16  *   All subproblems solved!    *
% 4.90/5.16  ********************************
% 4.90/5.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:37,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.98/5.16  
% 4.98/5.16  %**** Beginning of derivation protocol ****
% 4.98/5.16  % SZS output start CNFRefutation
% See solution above
% 4.98/5.16  
% 4.98/5.16  %**** End of derivation protocol ****
% 4.98/5.16  %**** no. of clauses in derivation: 38 ****
% 4.98/5.16  %**** clause counter: 37 ****
% 4.98/5.16  
% 4.98/5.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:37,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------