TSTP Solution File: DAT056^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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  : 300s
% DateTime : Mon May 20 19:47:56 EDT 2024

% Result   : Theorem 2.70s 1.88s
% Output   : Refutation 2.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   16 (   8 unt;   6 typ;   0 def)
%            Number of atoms       :   16 (  15 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  124 (   2   ~;   0   |;   0   &; 116   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   2 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0   ^  36   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(lst_type,type,
    lst: $tType ).

thf(a_type,type,
    a: $tType ).

thf(ap_type,type,
    ap: lst > lst > lst ).

thf(cns_type,type,
    cns: a > lst > lst ).

thf(nl_type,type,
    nl: lst ).

thf(xs_type,type,
    xs: lst ).

thf(1,conjecture,
    ! [A: lst,B: lst] :
      ( ( ap @ xs @ ( ap @ A @ B ) )
      = ( ap @ ( ap @ xs @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ! [A: lst,B: lst] :
        ( ( ap @ xs @ ( ap @ A @ B ) )
        = ( ap @ ( ap @ xs @ A ) @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: lst,B: lst] :
        ( ( ap @ xs @ ( ap @ A @ B ) )
        = ( ap @ ( ap @ xs @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: lst] :
      ( ! [B: lst,C: lst] :
          ( ( ap @ nl @ ( ap @ B @ C ) )
          = ( ap @ ( ap @ nl @ B ) @ C ) )
     => ( ! [B: a,C: lst] :
            ( ! [D: lst,E: lst] :
                ( ( ap @ C @ ( ap @ D @ E ) )
                = ( ap @ ( ap @ C @ D ) @ E ) )
           => ! [D: lst,E: lst] :
                ( ( ap @ ( cns @ B @ C ) @ ( ap @ D @ E ) )
                = ( ap @ ( ap @ ( cns @ B @ C ) @ D ) @ E ) ) )
       => ! [B: lst,C: lst] :
            ( ( ap @ A @ ( ap @ B @ C ) )
            = ( ap @ ( ap @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093) ).

thf(9,plain,
    ! [A: lst] :
      ( ! [B: lst,C: lst] :
          ( ( ap @ nl @ ( ap @ B @ C ) )
          = ( ap @ ( ap @ nl @ B ) @ C ) )
     => ( ! [B: a,C: lst] :
            ( ! [D: lst,E: lst] :
                ( ( ap @ C @ ( ap @ D @ E ) )
                = ( ap @ ( ap @ C @ D ) @ E ) )
           => ! [D: lst,E: lst] :
                ( ( ap @ ( cns @ B @ C ) @ ( ap @ D @ E ) )
                = ( ap @ ( ap @ ( cns @ B @ C ) @ D ) @ E ) ) )
       => ! [B: lst,C: lst] :
            ( ( ap @ A @ ( ap @ B @ C ) )
            = ( ap @ ( ap @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: lst,B: lst,C: a] :
      ( ( ap @ ( cns @ C @ B ) @ A )
      = ( cns @ C @ ( ap @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1p_Osimps_I2_J) ).

thf(16,plain,
    ! [A: lst,B: lst,C: a] :
      ( ( ap @ ( cns @ C @ B ) @ A )
      = ( cns @ C @ ( ap @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: lst] :
      ( ( ap @ nl @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2p_Osimps_I1_J) ).

thf(19,plain,
    ! [A: lst] :
      ( ( ap @ nl @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(22,plain,
    $false,
    inference(e,[status(thm)],[6,9,16,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Sun May 19 23:39:54 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.80/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.10/0.97  % [INFO] 	 Parsing done (135ms). 
% 1.10/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.50/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.50/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 1.50/1.29  % [INFO] 	 Scanning for conjecture ... 
% 1.68/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.79/1.38  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.79/1.42  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.79/1.42  % [INFO] 	 Type checking passed. 
% 1.79/1.42  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 2.70/1.83  % External prover 'e' found a proof!
% 2.70/1.83  % [INFO] 	 Killing All external provers ... 
% 2.70/1.84  % Time passed: 1414ms (effective reasoning time: 847ms)
% 2.70/1.84  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 2.70/1.84  % Axioms used in derivation (3): fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093, fact_1p_Osimps_I2_J, fact_2p_Osimps_I1_J
% 2.70/1.84  % No. of inferences in proof: 10
% 2.70/1.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1414 ms resp. 847 ms w/o parsing
% 2.97/1.92  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.97/1.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------