TSTP Solution File: LCL186-10 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL186-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n015.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 12:21:22 EDT 2022

% Result   : Unsatisfiable 0.73s 0.92s
% Output   : CNFRefutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   68 (  60 unt;   8 typ;   0 def)
%            Number of atoms       :  156 ( 100 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  534 (   6   ~;   0   |;   0   &; 528   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-4 aty)
%            Number of variables   :  110 (   0   ^ 110   !;   0   ?; 110   :)

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

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

thf(tp_not,type,
    not: $i > $i ).

thf(tp_or,type,
    or: $i > $i > $i ).

thf(tp_p,type,
    p: $i ).

thf(tp_q,type,
    q: $i ).

thf(tp_theorem,type,
    theorem: $i > $i ).

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

thf(1,axiom,
    ! [Y: $i,Z: $i,X: $i] :
      ( ( ifeq @ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ X ) @ Y ) ) @ true @ ( theorem @ ( or @ ( not @ X ) @ Z ) ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).

thf(2,axiom,
    ! [Y: $i,X: $i] :
      ( ( ifeq @ ( theorem @ Y ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ Y ) @ X ) ) @ true @ ( theorem @ X ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).

thf(3,axiom,
    ! [X: $i] :
      ( ( ifeq @ ( axiom @ X ) @ true @ ( theorem @ X ) @ true )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
      = true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

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,
    ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
 != true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

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

thf(14,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ( ifeq @ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ X ) @ Y ) ) @ true @ ( theorem @ ( or @ ( not @ X ) @ Z ) ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ! [Y: $i,X: $i] :
          ( ( ifeq @ ( theorem @ Y ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ Y ) @ X ) ) @ true @ ( theorem @ X ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ! [X: $i] :
          ( ( ifeq @ ( axiom @ X ) @ true @ ( theorem @ X ) @ true )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [A: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
          = true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(22,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(23,plain,
    ( ( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
       != true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

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

thf(25,plain,
    ( ( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
       != true ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(26,plain,
    ( ( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
       != true ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ifeq @ A @ A @ B @ C )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(28,plain,
    ( ( ! [A: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(29,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(30,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(31,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(32,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(33,plain,
    ( ( ! [X: $i] :
          ( ( ifeq @ ( axiom @ X ) @ true @ ( theorem @ X ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(34,plain,
    ( ( ! [Y: $i,X: $i] :
          ( ( ifeq @ ( theorem @ Y ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ Y ) @ X ) ) @ true @ ( theorem @ X ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(35,plain,
    ( ( ! [Y: $i,Z: $i,X: $i] :
          ( ( ifeq @ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ X ) @ Y ) ) @ true @ ( theorem @ ( or @ ( not @ X ) @ Z ) ) @ true ) @ true )
          = true ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

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

thf(37,plain,
    ( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
      = true )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(38,plain,
    ! [SV1: $i] :
      ( ( ! [SY20: $i,SY21: $i] :
            ( ( ifeq @ SV1 @ SV1 @ SY20 @ SY21 )
            = SY20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(39,plain,
    ! [SV2: $i] :
      ( ( ( axiom @ ( or @ ( not @ ( or @ SV2 @ SV2 ) ) @ SV2 ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(40,plain,
    ! [SV3: $i] :
      ( ( ! [SY22: $i] :
            ( ( axiom @ ( or @ ( not @ SV3 ) @ ( or @ SY22 @ SV3 ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(41,plain,
    ! [SV4: $i] :
      ( ( ! [SY23: $i] :
            ( ( axiom @ ( or @ ( not @ ( or @ SV4 @ SY23 ) ) @ ( or @ SY23 @ SV4 ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(42,plain,
    ! [SV5: $i] :
      ( ( ! [SY24: $i,SY25: $i] :
            ( ( axiom @ ( or @ ( not @ ( or @ SV5 @ ( or @ SY24 @ SY25 ) ) ) @ ( or @ SY24 @ ( or @ SV5 @ SY25 ) ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(43,plain,
    ! [SV6: $i] :
      ( ( ! [SY26: $i,SY27: $i] :
            ( ( axiom @ ( or @ ( not @ ( or @ ( not @ SV6 ) @ SY26 ) ) @ ( or @ ( not @ ( or @ SY27 @ SV6 ) ) @ ( or @ SY27 @ SY26 ) ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(44,plain,
    ! [SV7: $i] :
      ( ( ( ifeq @ ( axiom @ SV7 ) @ true @ ( theorem @ SV7 ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(45,plain,
    ! [SV8: $i] :
      ( ( ! [SY28: $i] :
            ( ( ifeq @ ( theorem @ SV8 ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SV8 ) @ SY28 ) ) @ true @ ( theorem @ SY28 ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(46,plain,
    ! [SV9: $i] :
      ( ( ! [SY29: $i,SY30: $i] :
            ( ( ifeq @ ( theorem @ ( or @ ( not @ SV9 ) @ SY29 ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SY30 ) @ SV9 ) ) @ true @ ( theorem @ ( or @ ( not @ SY30 ) @ SY29 ) ) @ true ) @ true )
            = true ) )
      = $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,SV1: $i] :
      ( ( ! [SY31: $i] :
            ( ( ifeq @ SV1 @ SV1 @ SV10 @ SY31 )
            = SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(49,plain,
    ! [SV11: $i,SV3: $i] :
      ( ( ( axiom @ ( or @ ( not @ SV3 ) @ ( or @ SV11 @ SV3 ) ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(50,plain,
    ! [SV12: $i,SV4: $i] :
      ( ( ( axiom @ ( or @ ( not @ ( or @ SV4 @ SV12 ) ) @ ( or @ SV12 @ SV4 ) ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(51,plain,
    ! [SV13: $i,SV5: $i] :
      ( ( ! [SY32: $i] :
            ( ( axiom @ ( or @ ( not @ ( or @ SV5 @ ( or @ SV13 @ SY32 ) ) ) @ ( or @ SV13 @ ( or @ SV5 @ SY32 ) ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(52,plain,
    ! [SV14: $i,SV6: $i] :
      ( ( ! [SY33: $i] :
            ( ( axiom @ ( or @ ( not @ ( or @ ( not @ SV6 ) @ SV14 ) ) @ ( or @ ( not @ ( or @ SY33 @ SV6 ) ) @ ( or @ SY33 @ SV14 ) ) ) )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(53,plain,
    ! [SV15: $i,SV8: $i] :
      ( ( ( ifeq @ ( theorem @ SV8 ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SV8 ) @ SV15 ) ) @ true @ ( theorem @ SV15 ) @ true ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(54,plain,
    ! [SV16: $i,SV9: $i] :
      ( ( ! [SY34: $i] :
            ( ( ifeq @ ( theorem @ ( or @ ( not @ SV9 ) @ SV16 ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SY34 ) @ SV9 ) ) @ true @ ( theorem @ ( or @ ( not @ SY34 ) @ SV16 ) ) @ true ) @ true )
            = true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(55,plain,
    ! [SV17: $i,SV10: $i,SV1: $i] :
      ( ( ( ifeq @ SV1 @ SV1 @ SV10 @ SV17 )
        = SV10 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(56,plain,
    ! [SV18: $i,SV13: $i,SV5: $i] :
      ( ( ( axiom @ ( or @ ( not @ ( or @ SV5 @ ( or @ SV13 @ SV18 ) ) ) @ ( or @ SV13 @ ( or @ SV5 @ SV18 ) ) ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV19: $i,SV14: $i,SV6: $i] :
      ( ( ( axiom @ ( or @ ( not @ ( or @ ( not @ SV6 ) @ SV14 ) ) @ ( or @ ( not @ ( or @ SV19 @ SV6 ) ) @ ( or @ SV19 @ SV14 ) ) ) )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV20: $i,SV16: $i,SV9: $i] :
      ( ( ( ifeq @ ( theorem @ ( or @ ( not @ SV9 ) @ SV16 ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SV20 ) @ SV9 ) ) @ true @ ( theorem @ ( or @ ( not @ SV20 ) @ SV16 ) ) @ true ) @ true )
        = true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(59,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[37,58,57,56,55,53,50,49,47,44,39]) ).

thf(60,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem  : LCL186-10 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.09  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.29  % Computer : n015.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Mon Jul  4 03:58:16 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.09/0.30  
% 0.09/0.30   No.of.Axioms: 10
% 0.09/0.30  
% 0.09/0.30   Length.of.Defs: 0
% 0.09/0.30  
% 0.09/0.30   Contains.Choice.Funs: false
% 0.09/0.30  (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)...
% 0.73/0.92  
% 0.73/0.92  ********************************
% 0.73/0.92  *   All subproblems solved!    *
% 0.73/0.92  ********************************
% 0.73/0.92  % SZS status Unsatisfiable for /export/starexec/sandbox/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:59,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.73/0.93  
% 0.73/0.93  %**** Beginning of derivation protocol ****
% 0.73/0.93  % SZS output start CNFRefutation
% See solution above
% 0.73/0.93  
% 0.73/0.93  %**** End of derivation protocol ****
% 0.73/0.93  %**** no. of clauses in derivation: 60 ****
% 0.73/0.93  %**** clause counter: 59 ****
% 0.73/0.93  
% 0.73/0.93  % SZS status Unsatisfiable for /export/starexec/sandbox/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:59,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------