TSTP Solution File: COL124-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : COL124-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : Fri Jul 15 00:34:55 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   37 (  23 unt;   9 typ;   0 def)
%            Number of atoms       :  108 (  30 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :  453 (  23   ~;  20   |;   0   &; 410   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   6 con; 0-4 aty)
%            Number of variables   :   45 (   0   ^  45   !;   0   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_Comb_OI,type,
    c_Comb_OI: $i ).

thf(tp_c_Comb_Ocomb_OK,type,
    c_Comb_Ocomb_OK: $i ).

thf(tp_c_Comb_Ocomb_Oop_A_D_D,type,
    c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).

thf(tp_c_Comb_Ocontract,type,
    c_Comb_Ocontract: $i ).

thf(tp_c_Pair,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(tp_c_in,type,
    c_in: $i > $i > $i > $o ).

thf(tp_tc_Comb_Ocomb,type,
    tc_Comb_Ocomb: $i ).

thf(tp_tc_prod,type,
    tc_prod: $i > $i > $i ).

thf(tp_v_x,type,
    v_x: $i > $i > $i > $i ).

thf(1,axiom,
    ! [V_x: $i,V_y: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ V_x ) @ V_y ) @ V_x @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocontract_OK_0) ).

thf(2,axiom,
    ! [V_z: $i] :
      ~ ( c_in @ ( c_Pair @ c_Comb_OI @ V_z @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OI__contract__E_0) ).

thf(3,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(4,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[3]) ).

thf(5,negated_conjecture,
    ! [V_V: $i,V_U: $i,V_W: $i] :
      ( ( c_in @ ( c_Pair @ V_V @ ( v_x @ V_U @ V_V @ V_W ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
      | ~ ( c_in @ ( c_Pair @ V_U @ V_W @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
      | ~ ( c_in @ ( c_Pair @ V_U @ V_V @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(6,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ! [V_x: $i,V_y: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ V_x ) @ V_y ) @ V_x @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(8,plain,
    ( ( ! [V_z: $i] :
          ~ ( c_in @ ( c_Pair @ c_Comb_OI @ V_z @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ! [V_V: $i,V_U: $i,V_W: $i] :
          ( ( c_in @ ( c_Pair @ V_V @ ( v_x @ V_U @ V_V @ V_W ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
          | ~ ( c_in @ ( c_Pair @ V_U @ V_W @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
          | ~ ( c_in @ ( c_Pair @ V_U @ V_V @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(10,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(11,plain,
    ( ( ! [V_V: $i,V_U: $i,V_W: $i] :
          ( ( c_in @ ( c_Pair @ V_V @ ( v_x @ V_U @ V_V @ V_W ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
          | ~ ( c_in @ ( c_Pair @ V_U @ V_W @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
          | ~ ( c_in @ ( c_Pair @ V_U @ V_V @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ! [V_z: $i] :
          ~ ( c_in @ ( c_Pair @ c_Comb_OI @ V_z @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(13,plain,
    ( ( ! [V_x: $i,V_y: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ V_x ) @ V_y ) @ V_x @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(14,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ! [SY6: $i,SY7: $i] :
            ( ( c_in @ ( c_Pair @ SV1 @ ( v_x @ SY6 @ SV1 @ SY7 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
            | ~ ( c_in @ ( c_Pair @ SY6 @ SY7 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
            | ~ ( c_in @ ( c_Pair @ SY6 @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(16,plain,
    ! [SV2: $i] :
      ( ( ~ ( c_in @ ( c_Pair @ c_Comb_OI @ SV2 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
    ! [SV3: $i] :
      ( ( ! [SY8: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ SV3 ) @ SY8 ) @ SV3 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(18,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(19,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ! [SY9: $i] :
            ( ( c_in @ ( c_Pair @ SV1 @ ( v_x @ SV4 @ SV1 @ SY9 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
            | ~ ( c_in @ ( c_Pair @ SV4 @ SY9 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
            | ~ ( c_in @ ( c_Pair @ SV4 @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(20,plain,
    ! [SV2: $i] :
      ( ( c_in @ ( c_Pair @ c_Comb_OI @ SV2 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(21,plain,
    ! [SV5: $i,SV3: $i] :
      ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OK @ SV3 ) @ SV5 ) @ SV3 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(22,plain,
    ! [SV6: $i,SV4: $i,SV1: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1 @ ( v_x @ SV4 @ SV1 @ SV6 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        | ~ ( c_in @ ( c_Pair @ SV4 @ SV6 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        | ~ ( c_in @ ( c_Pair @ SV4 @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV6: $i,SV4: $i,SV1: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1 @ ( v_x @ SV4 @ SV1 @ SV6 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        = $true )
      | ( ( ~ ( c_in @ ( c_Pair @ SV4 @ SV6 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
          | ~ ( c_in @ ( c_Pair @ SV4 @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(24,plain,
    ! [SV1: $i,SV6: $i,SV4: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ SV4 @ SV6 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
        = $true )
      | ( ( ~ ( c_in @ ( c_Pair @ SV4 @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1 @ ( v_x @ SV4 @ SV1 @ SV6 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(25,plain,
    ! [SV1: $i,SV6: $i,SV4: $i] :
      ( ( ( c_in @ ( c_Pair @ SV4 @ SV6 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        = $false )
      | ( ( ~ ( c_in @ ( c_Pair @ SV4 @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1 @ ( v_x @ SV4 @ SV1 @ SV6 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(26,plain,
    ! [SV6: $i,SV1: $i,SV4: $i] :
      ( ( ( c_in @ ( c_Pair @ SV4 @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV4 @ SV6 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1 @ ( v_x @ SV4 @ SV1 @ SV6 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Ocontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(27,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[18,26,21,20]) ).

thf(28,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COL124-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % 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 : Tue May 31 13:29:56 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 3
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:3,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:5,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.39  
% 0.13/0.39  ********************************
% 0.13/0.39  *   All subproblems solved!    *
% 0.13/0.39  ********************************
% 0.13/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.39  
% 0.13/0.39  %**** Beginning of derivation protocol ****
% 0.13/0.39  % SZS output start CNFRefutation
% See solution above
% 0.13/0.39  
% 0.13/0.39  %**** End of derivation protocol ****
% 0.13/0.39  %**** no. of clauses in derivation: 28 ****
% 0.13/0.39  %**** clause counter: 27 ****
% 0.13/0.39  
% 0.13/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------