TSTP Solution File: GRP682-11 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP682-11 : 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 : n016.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 10:19:32 EDT 2022

% Result   : Unsatisfiable 0.77s 0.94s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   56 (  50 unt;   6 typ;   0 def)
%            Number of atoms       :  130 (  82 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  462 (   6   ~;   0   |;   0   &; 456   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   94 (   0   ^  94   !;   0   ?;  94   :)

% 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_x0,type,
    x0: $i ).

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

thf(tp_x2,type,
    x2: $i ).

thf(1,axiom,
    ! [A: $i,B: $i] :
      ( ( ld @ A @ ( mult @ A @ ( ld @ B @ B ) ) )
      = ( rd @ ( mult @ ( rd @ A @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).

thf(2,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( rd @ ( mult @ ( mult @ A @ B ) @ ( rd @ C @ D ) ) @ ( rd @ C @ D ) )
      = ( mult @ A @ ( rd @ ( mult @ B @ D ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ld @ ( ld @ A @ B ) @ ( mult @ ( ld @ A @ B ) @ ( mult @ C @ D ) ) )
      = ( mult @ ( ld @ A @ ( mult @ A @ C ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( mult @ ( rd @ A @ B ) @ B )
      = ( rd @ ( mult @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( mult @ A @ ( ld @ A @ B ) )
      = ( ld @ A @ ( mult @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( rd @ ( mult @ A @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( ld @ A @ ( mult @ A @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

thf(8,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(9,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[8]) ).

thf(10,negated_conjecture,
    ( ld @ ( rd @ x0 @ x1 ) @ ( mult @ ( rd @ x0 @ x1 ) @ x2 ) )
 != ( ld @ x0 @ ( mult @ x0 @ x2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

thf(11,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ld @ A @ ( mult @ A @ ( ld @ B @ B ) ) )
          = ( rd @ ( mult @ ( rd @ A @ A ) @ B ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(13,plain,
    ( ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ( rd @ ( mult @ ( mult @ A @ B ) @ ( rd @ C @ D ) ) @ ( rd @ C @ D ) )
          = ( mult @ A @ ( rd @ ( mult @ B @ D ) @ D ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(14,plain,
    ( ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ( ld @ ( ld @ A @ B ) @ ( mult @ ( ld @ A @ B ) @ ( mult @ C @ D ) ) )
          = ( mult @ ( ld @ A @ ( mult @ A @ C ) ) @ D ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(15,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( mult @ ( rd @ A @ B ) @ B )
          = ( rd @ ( mult @ A @ B ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(16,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( mult @ A @ ( ld @ A @ B ) )
          = ( ld @ A @ ( mult @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(17,plain,
    ( ( ! [A: $i] :
          ( ( rd @ ( mult @ A @ A ) @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(18,plain,
    ( ( ! [A: $i] :
          ( ( ld @ A @ ( mult @ A @ A ) )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(19,plain,
    ( ( ( ( ld @ ( rd @ x0 @ x1 ) @ ( mult @ ( rd @ x0 @ x1 ) @ x2 ) )
       != ( ld @ x0 @ ( mult @ x0 @ x2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(20,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[11]) ).

thf(21,plain,
    ( ( ( ( ld @ ( rd @ x0 @ x1 ) @ ( mult @ ( rd @ x0 @ x1 ) @ x2 ) )
       != ( ld @ x0 @ ( mult @ x0 @ x2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(22,plain,
    ( ( ( ( ld @ ( rd @ x0 @ x1 ) @ ( mult @ ( rd @ x0 @ x1 ) @ x2 ) )
       != ( ld @ x0 @ ( mult @ x0 @ x2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(23,plain,
    ( ( ! [A: $i] :
          ( ( ld @ A @ ( mult @ A @ A ) )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(24,plain,
    ( ( ! [A: $i] :
          ( ( rd @ ( mult @ A @ A ) @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( mult @ A @ ( ld @ A @ B ) )
          = ( ld @ A @ ( mult @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(26,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( mult @ ( rd @ A @ B ) @ B )
          = ( rd @ ( mult @ A @ B ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ( ld @ ( ld @ A @ B ) @ ( mult @ ( ld @ A @ B ) @ ( mult @ C @ D ) ) )
          = ( mult @ ( ld @ A @ ( mult @ A @ C ) ) @ D ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(28,plain,
    ( ( ! [A: $i,B: $i,C: $i,D: $i] :
          ( ( rd @ ( mult @ ( mult @ A @ B ) @ ( rd @ C @ D ) ) @ ( rd @ C @ D ) )
          = ( mult @ A @ ( rd @ ( mult @ B @ D ) @ D ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(29,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ld @ A @ ( mult @ A @ ( ld @ B @ B ) ) )
          = ( rd @ ( mult @ ( rd @ A @ A ) @ B ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(30,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(31,plain,
    ( ( ( ld @ ( rd @ x0 @ x1 ) @ ( mult @ ( rd @ x0 @ x1 ) @ x2 ) )
      = ( ld @ x0 @ ( mult @ x0 @ x2 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(32,plain,
    ! [SV1: $i] :
      ( ( ( ld @ SV1 @ ( mult @ SV1 @ SV1 ) )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(33,plain,
    ! [SV2: $i] :
      ( ( ( rd @ ( mult @ SV2 @ SV2 ) @ SV2 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( ! [SY16: $i] :
            ( ( mult @ SV3 @ ( ld @ SV3 @ SY16 ) )
            = ( ld @ SV3 @ ( mult @ SV3 @ SY16 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(35,plain,
    ! [SV4: $i] :
      ( ( ! [SY17: $i] :
            ( ( mult @ ( rd @ SV4 @ SY17 ) @ SY17 )
            = ( rd @ ( mult @ SV4 @ SY17 ) @ SY17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(36,plain,
    ! [SV5: $i] :
      ( ( ! [SY18: $i,SY19: $i,SY20: $i] :
            ( ( ld @ ( ld @ SV5 @ SY18 ) @ ( mult @ ( ld @ SV5 @ SY18 ) @ ( mult @ SY19 @ SY20 ) ) )
            = ( mult @ ( ld @ SV5 @ ( mult @ SV5 @ SY19 ) ) @ SY20 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(37,plain,
    ! [SV6: $i] :
      ( ( ! [SY21: $i,SY22: $i,SY23: $i] :
            ( ( rd @ ( mult @ ( mult @ SV6 @ SY21 ) @ ( rd @ SY22 @ SY23 ) ) @ ( rd @ SY22 @ SY23 ) )
            = ( mult @ SV6 @ ( rd @ ( mult @ SY21 @ SY23 ) @ SY23 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(38,plain,
    ! [SV7: $i] :
      ( ( ! [SY24: $i] :
            ( ( ld @ SV7 @ ( mult @ SV7 @ ( ld @ SY24 @ SY24 ) ) )
            = ( rd @ ( mult @ ( rd @ SV7 @ SV7 ) @ SY24 ) @ SY24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(39,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(40,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ( mult @ SV3 @ ( ld @ SV3 @ SV8 ) )
        = ( ld @ SV3 @ ( mult @ SV3 @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV9: $i,SV4: $i] :
      ( ( ( mult @ ( rd @ SV4 @ SV9 ) @ SV9 )
        = ( rd @ ( mult @ SV4 @ SV9 ) @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV10: $i,SV5: $i] :
      ( ( ! [SY25: $i,SY26: $i] :
            ( ( ld @ ( ld @ SV5 @ SV10 ) @ ( mult @ ( ld @ SV5 @ SV10 ) @ ( mult @ SY25 @ SY26 ) ) )
            = ( mult @ ( ld @ SV5 @ ( mult @ SV5 @ SY25 ) ) @ SY26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV11: $i,SV6: $i] :
      ( ( ! [SY27: $i,SY28: $i] :
            ( ( rd @ ( mult @ ( mult @ SV6 @ SV11 ) @ ( rd @ SY27 @ SY28 ) ) @ ( rd @ SY27 @ SY28 ) )
            = ( mult @ SV6 @ ( rd @ ( mult @ SV11 @ SY28 ) @ SY28 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV12: $i,SV7: $i] :
      ( ( ( ld @ SV7 @ ( mult @ SV7 @ ( ld @ SV12 @ SV12 ) ) )
        = ( rd @ ( mult @ ( rd @ SV7 @ SV7 ) @ SV12 ) @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV13: $i,SV10: $i,SV5: $i] :
      ( ( ! [SY29: $i] :
            ( ( ld @ ( ld @ SV5 @ SV10 ) @ ( mult @ ( ld @ SV5 @ SV10 ) @ ( mult @ SV13 @ SY29 ) ) )
            = ( mult @ ( ld @ SV5 @ ( mult @ SV5 @ SV13 ) ) @ SY29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(46,plain,
    ! [SV14: $i,SV11: $i,SV6: $i] :
      ( ( ! [SY30: $i] :
            ( ( rd @ ( mult @ ( mult @ SV6 @ SV11 ) @ ( rd @ SV14 @ SY30 ) ) @ ( rd @ SV14 @ SY30 ) )
            = ( mult @ SV6 @ ( rd @ ( mult @ SV11 @ SY30 ) @ SY30 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(47,plain,
    ! [SV15: $i,SV13: $i,SV10: $i,SV5: $i] :
      ( ( ( ld @ ( ld @ SV5 @ SV10 ) @ ( mult @ ( ld @ SV5 @ SV10 ) @ ( mult @ SV13 @ SV15 ) ) )
        = ( mult @ ( ld @ SV5 @ ( mult @ SV5 @ SV13 ) ) @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(48,plain,
    ! [SV16: $i,SV14: $i,SV11: $i,SV6: $i] :
      ( ( ( rd @ ( mult @ ( mult @ SV6 @ SV11 ) @ ( rd @ SV14 @ SV16 ) ) @ ( rd @ SV14 @ SV16 ) )
        = ( mult @ SV6 @ ( rd @ ( mult @ SV11 @ SV16 ) @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(49,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[31,48,47,44,41,40,39,33,32]) ).

thf(50,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[49]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP682-11 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 07:41:30 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.36  
% 0.20/0.36   No.of.Axioms: 8
% 0.20/0.36  
% 0.20/0.36   Length.of.Defs: 0
% 0.20/0.36  
% 0.20/0.36   Contains.Choice.Funs: false
% 0.20/0.36  (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.77/0.94  
% 0.77/0.94  ********************************
% 0.77/0.94  *   All subproblems solved!    *
% 0.77/0.94  ********************************
% 0.77/0.94  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.77/0.94  
% 0.77/0.94  %**** Beginning of derivation protocol ****
% 0.77/0.94  % SZS output start CNFRefutation
% See solution above
% 0.77/0.94  
% 0.77/0.94  %**** End of derivation protocol ****
% 0.77/0.94  %**** no. of clauses in derivation: 50 ****
% 0.77/0.94  %**** clause counter: 49 ****
% 0.77/0.94  
% 0.77/0.94  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:8,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:49,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------