TSTP Solution File: LCL026-10 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL026-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n013.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 : Sun Jul 17 12:20:03 EDT 2022

% Result   : Unsatisfiable 41.45s 41.69s
% Output   : CNFRefutation 41.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   46 (  39 unt;   7 typ;   0 def)
%            Number of atoms       :  101 (  62 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  261 (   6   ~;   0   |;   0   &; 255   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-4 aty)
%            Number of variables   :   60 (   0   ^  60   !;   0   ?;  60   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_b,type,
    b: $i ).

thf(tp_falsehood,type,
    falsehood: $i ).

thf(tp_ifeq,type,
    ifeq: $i > $i > $i > $i > $i ).

thf(tp_implies,type,
    implies: $i > $i > $i ).

thf(tp_is_a_theorem,type,
    is_a_theorem: $i > $i ).

thf(tp_true,type,
    true: $i ).

thf(1,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ Y @ Z ) ) @ ( implies @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_6) ).

thf(2,axiom,
    ! [X: $i] :
      ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ X @ falsehood ) @ falsehood ) @ X ) )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_5) ).

thf(3,axiom,
    ! [X: $i,Y: $i] :
      ( ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_2) ).

thf(4,axiom,
    ! [X: $i,Y: $i] :
      ( ( ifeq @ ( is_a_theorem @ ( implies @ X @ Y ) ) @ true @ ( ifeq @ ( is_a_theorem @ X ) @ true @ ( is_a_theorem @ Y ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).

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

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,
    ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ a ) @ a ) )
 != true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c0_3) ).

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

thf(10,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ Y @ Z ) ) @ ( implies @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(11,plain,
    ( ( ! [X: $i] :
          ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ X @ falsehood ) @ falsehood ) @ X ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(12,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(13,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ifeq @ ( is_a_theorem @ ( implies @ X @ Y ) ) @ true @ ( ifeq @ ( is_a_theorem @ X ) @ true @ ( is_a_theorem @ Y ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

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

thf(15,plain,
    ( ( ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ a ) @ a ) )
       != true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

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

thf(17,plain,
    ( ( ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ a ) @ a ) )
       != true ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(18,plain,
    ( ( ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ a ) @ a ) )
       != true ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

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

thf(20,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ifeq @ ( is_a_theorem @ ( implies @ X @ Y ) ) @ true @ ( ifeq @ ( is_a_theorem @ X ) @ true @ ( is_a_theorem @ Y ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(21,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(22,plain,
    ( ( ! [X: $i] :
          ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ X @ falsehood ) @ falsehood ) @ X ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(23,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ Y @ Z ) ) @ ( implies @ ( implies @ X @ Y ) @ ( implies @ X @ Z ) ) ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

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

thf(25,plain,
    ( ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ a ) @ a ) )
      = true )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(26,plain,
    ! [SV1: $i] :
      ( ( ! [SY11: $i,SY12: $i] :
            ( ( ifeq @ SV1 @ SV1 @ SY11 @ SY12 )
            = SY11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(27,plain,
    ! [SV2: $i] :
      ( ( ! [SY13: $i] :
            ( ( ifeq @ ( is_a_theorem @ ( implies @ SV2 @ SY13 ) ) @ true @ ( ifeq @ ( is_a_theorem @ SV2 ) @ true @ ( is_a_theorem @ SY13 ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(28,plain,
    ! [SV3: $i] :
      ( ( ! [SY14: $i] :
            ( ( is_a_theorem @ ( implies @ SV3 @ ( implies @ SY14 @ SV3 ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(29,plain,
    ! [SV4: $i] :
      ( ( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ SV4 @ falsehood ) @ falsehood ) @ SV4 ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(30,plain,
    ! [SV5: $i] :
      ( ( ! [SY15: $i,SY16: $i] :
            ( ( is_a_theorem @ ( implies @ ( implies @ SV5 @ ( implies @ SY15 @ SY16 ) ) @ ( implies @ ( implies @ SV5 @ SY15 ) @ ( implies @ SV5 @ SY16 ) ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

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

thf(32,plain,
    ! [SV6: $i,SV1: $i] :
      ( ( ! [SY17: $i] :
            ( ( ifeq @ SV1 @ SV1 @ SV6 @ SY17 )
            = SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(33,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ( ifeq @ ( is_a_theorem @ ( implies @ SV2 @ SV7 ) ) @ true @ ( ifeq @ ( is_a_theorem @ SV2 ) @ true @ ( is_a_theorem @ SV7 ) @ true ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(34,plain,
    ! [SV8: $i,SV3: $i] :
      ( ( ( is_a_theorem @ ( implies @ SV3 @ ( implies @ SV8 @ SV3 ) ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV9: $i,SV5: $i] :
      ( ( ! [SY18: $i] :
            ( ( is_a_theorem @ ( implies @ ( implies @ SV5 @ ( implies @ SV9 @ SY18 ) ) @ ( implies @ ( implies @ SV5 @ SV9 ) @ ( implies @ SV5 @ SY18 ) ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(36,plain,
    ! [SV10: $i,SV6: $i,SV1: $i] :
      ( ( ( ifeq @ SV1 @ SV1 @ SV6 @ SV10 )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV11: $i,SV9: $i,SV5: $i] :
      ( ( ( is_a_theorem @ ( implies @ ( implies @ SV5 @ ( implies @ SV9 @ SV11 ) ) @ ( implies @ ( implies @ SV5 @ SV9 ) @ ( implies @ SV5 @ SV11 ) ) ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(38,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[25,37,36,34,33,31,29]) ).

thf(39,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL026-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n013.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 Jul  4 13:45:59 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 6
% 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: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)..
% 41.45/41.69  
% 41.45/41.69  ********************************
% 41.45/41.69  *   All subproblems solved!    *
% 41.45/41.69  ********************************
% 41.45/41.69  % 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:38,loop_count:0,foatp_calls:1,translation:fof_full)
% 41.45/41.69  
% 41.45/41.69  %**** Beginning of derivation protocol ****
% 41.45/41.69  % SZS output start CNFRefutation
% See solution above
% 41.45/41.69  
% 41.45/41.69  %**** End of derivation protocol ****
% 41.45/41.69  %**** no. of clauses in derivation: 39 ****
% 41.45/41.69  %**** clause counter: 38 ****
% 41.45/41.69  
% 41.45/41.69  % 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:38,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------