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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n003.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 19:48:45 EDT 2024

% Result   : Theorem 16.79s 4.00s
% Output   : Refutation 16.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   50 (  21 unt;  14 typ;   0 def)
%            Number of atoms       :   65 (  64 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  578 (  21   ~;  20   |;   0   &; 528   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   2 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;  11 con; 0-2 aty)
%            Number of variables   :  119 (   0   ^ 119   !;   0   ?; 119   :)

% 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(sk1_type,type,
    sk1: lst ).

thf(sk2_type,type,
    sk2: lst ).

thf(sk3_type,type,
    sk3: lst ).

thf(sk4_type,type,
    sk4: lst ).

thf(sk5_type,type,
    sk5: a ).

thf(sk6_type,type,
    sk6: lst ).

thf(sk7_type,type,
    sk7: lst ).

thf(sk8_type,type,
    sk8: 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(7,plain,
    ( ( ap @ xs @ ( ap @ sk1 @ sk2 ) )
   != ( ap @ ( ap @ xs @ sk1 ) @ sk2 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ap @ ( ap @ xs @ sk1 ) @ sk2 )
   != ( ap @ xs @ ( ap @ sk1 @ sk2 ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

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

thf(11,plain,
    ! [C: lst,B: lst,A: lst] :
      ( ( ( ap @ nl @ ( ap @ sk3 @ sk4 ) )
       != ( ap @ ( ap @ nl @ sk3 ) @ sk4 ) )
      | ( ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) )
       != ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 ) )
      | ( ( ap @ A @ ( ap @ B @ C ) )
        = ( ap @ ( ap @ A @ B ) @ C ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(13,plain,
    ! [C: lst,B: lst,A: lst] :
      ( ( ( ap @ ( ap @ nl @ sk3 ) @ sk4 )
       != ( ap @ nl @ ( ap @ sk3 @ sk4 ) ) )
      | ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
       != ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
      | ( ( ap @ ( ap @ A @ B ) @ C )
        = ( ap @ A @ ( ap @ B @ C ) ) ) ),
    inference(lifteq,[status(thm)],[11]) ).

thf(14,plain,
    ! [C: lst,B: lst,A: lst] :
      ( ( ( ap @ ( ap @ nl @ sk3 ) @ sk4 )
       != ( ap @ nl @ ( ap @ sk3 @ sk4 ) ) )
      | ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
       != ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
      | ( ( ap @ ( ap @ A @ B ) @ C )
        = ( ap @ A @ ( ap @ B @ C ) ) ) ),
    inference(simp,[status(thm)],[13]) ).

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(20,plain,
    ! [A: lst] :
      ( ( ap @ nl @ A )
      = A ),
    inference(cnf,[status(esa)],[19]) ).

thf(21,plain,
    ! [A: lst] :
      ( ( ap @ nl @ A )
      = A ),
    inference(lifteq,[status(thm)],[20]) ).

thf(91,plain,
    ! [C: lst,B: lst,A: lst] :
      ( ( ( ap @ sk3 @ sk4 )
       != ( ap @ sk3 @ sk4 ) )
      | ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
       != ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
      | ( ( ap @ ( ap @ A @ B ) @ C )
        = ( ap @ A @ ( ap @ B @ C ) ) ) ),
    inference(rewrite,[status(thm)],[14,21]) ).

thf(92,plain,
    ! [C: lst,B: lst,A: lst] :
      ( ( ( ap @ ( ap @ ( cns @ sk5 @ sk6 ) @ sk7 ) @ sk8 )
       != ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
      | ( ( ap @ ( ap @ A @ B ) @ C )
        = ( ap @ A @ ( ap @ B @ C ) ) ) ),
    inference(simp,[status(thm)],[91]) ).

thf(12,plain,
    ! [E: lst,D: lst,C: lst,B: lst,A: lst] :
      ( ( ( ap @ nl @ ( ap @ sk3 @ sk4 ) )
       != ( ap @ ( ap @ nl @ sk3 ) @ sk4 ) )
      | ( ( ap @ sk6 @ ( ap @ A @ B ) )
        = ( ap @ ( ap @ sk6 @ A ) @ B ) )
      | ( ( ap @ C @ ( ap @ D @ E ) )
        = ( ap @ ( ap @ C @ D ) @ E ) ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(15,plain,
    ! [E: lst,D: lst,C: lst,B: lst,A: lst] :
      ( ( ( ap @ ( ap @ nl @ sk3 ) @ sk4 )
       != ( ap @ nl @ ( ap @ sk3 @ sk4 ) ) )
      | ( ( ap @ ( ap @ sk6 @ A ) @ B )
        = ( ap @ sk6 @ ( ap @ A @ B ) ) )
      | ( ( ap @ ( ap @ C @ D ) @ E )
        = ( ap @ C @ ( ap @ D @ E ) ) ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(541,plain,
    ! [E: lst,D: lst,C: lst,B: lst,A: lst] :
      ( ( ( ap @ sk3 @ sk4 )
       != ( ap @ sk3 @ sk4 ) )
      | ( ( ap @ ( ap @ sk6 @ A ) @ B )
        = ( ap @ sk6 @ ( ap @ A @ B ) ) )
      | ( ( ap @ ( ap @ C @ D ) @ E )
        = ( ap @ C @ ( ap @ D @ E ) ) ) ),
    inference(rewrite,[status(thm)],[15,21]) ).

thf(542,plain,
    ! [E: lst,D: lst,C: lst,B: lst,A: lst] :
      ( ( ( ap @ ( ap @ sk6 @ A ) @ B )
        = ( ap @ sk6 @ ( ap @ A @ B ) ) )
      | ( ( ap @ ( ap @ C @ D ) @ E )
        = ( ap @ C @ ( ap @ D @ E ) ) ) ),
    inference(simp,[status(thm)],[541]) ).

thf(634,plain,
    ! [E: lst,D: lst,C: lst,B: lst,A: lst] :
      ( ( ( ap @ ( ap @ sk6 @ A ) @ B )
        = ( ap @ sk6 @ ( ap @ A @ B ) ) )
      | ( ( ap @ ( ap @ C @ D ) @ E )
       != ( ap @ ( ap @ sk6 @ A ) @ B ) )
      | ( ( ap @ C @ ( ap @ D @ E ) )
       != ( ap @ sk6 @ ( ap @ A @ B ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[542]) ).

thf(637,plain,
    ! [B: lst,A: lst] :
      ( ( ap @ ( ap @ sk6 @ A ) @ B )
      = ( ap @ sk6 @ ( ap @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( sk6 ))]]) ).

thf(773,plain,
    ! [B: lst,A: lst] :
      ( ( ap @ ( ap @ sk6 @ A ) @ B )
      = ( ap @ sk6 @ ( ap @ A @ B ) ) ),
    inference(simp,[status(thm)],[637]) ).

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(17,plain,
    ! [C: a,B: lst,A: lst] :
      ( ( ap @ ( cns @ C @ B ) @ A )
      = ( cns @ C @ ( ap @ B @ A ) ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(18,plain,
    ! [C: a,B: lst,A: lst] :
      ( ( cns @ C @ ( ap @ B @ A ) )
      = ( ap @ ( cns @ C @ B ) @ A ) ),
    inference(lifteq,[status(thm)],[17]) ).

thf(795,plain,
    ! [E: a,D: lst,C: lst,B: lst,A: lst] :
      ( ( ( cns @ E @ ( ap @ sk6 @ ( ap @ A @ B ) ) )
        = ( ap @ ( cns @ E @ D ) @ C ) )
      | ( ( ap @ ( ap @ sk6 @ A ) @ B )
       != ( ap @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[773,18]) ).

thf(796,plain,
    ! [C: lst,B: a,A: lst] :
      ( ( cns @ B @ ( ap @ sk6 @ ( ap @ C @ A ) ) )
      = ( ap @ ( cns @ B @ ( ap @ sk6 @ C ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[795:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( ap @ sk6 @ G )),bind(E,$thf( E ))]]) ).

thf(871,plain,
    ! [C: lst,B: a,A: lst] :
      ( ( cns @ B @ ( ap @ sk6 @ ( ap @ C @ A ) ) )
      = ( ap @ ( cns @ B @ ( ap @ sk6 @ C ) ) @ A ) ),
    inference(simp,[status(thm)],[796]) ).

thf(3265,plain,
    ! [C: lst,B: a,A: lst] :
      ( ( ap @ ( ap @ ( cns @ B @ sk6 ) @ C ) @ A )
      = ( ap @ ( cns @ B @ sk6 ) @ ( ap @ C @ A ) ) ),
    inference(rewrite,[status(thm)],[871,18]) ).

thf(3266,plain,
    ! [C: lst,B: lst,A: lst] :
      ( ( ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) )
       != ( ap @ ( cns @ sk5 @ sk6 ) @ ( ap @ sk7 @ sk8 ) ) )
      | ( ( ap @ ( ap @ A @ B ) @ C )
        = ( ap @ A @ ( ap @ B @ C ) ) ) ),
    inference(rewrite,[status(thm)],[92,3265]) ).

thf(3267,plain,
    ! [C: lst,B: lst,A: lst] :
      ( ( ap @ ( ap @ A @ B ) @ C )
      = ( ap @ A @ ( ap @ B @ C ) ) ),
    inference(simp,[status(thm)],[3266]) ).

thf(3499,plain,
    ( ( ap @ xs @ ( ap @ sk1 @ sk2 ) )
   != ( ap @ xs @ ( ap @ sk1 @ sk2 ) ) ),
    inference(rewrite,[status(thm)],[8,3267]) ).

thf(3500,plain,
    $false,
    inference(simp,[status(thm)],[3499]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : DAT056^1 : TPTP v8.2.0. Released v5.4.0.
% 0.16/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n003.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 23:39:53 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.01  % [INFO] 	 Parsing done (117ms). 
% 1.25/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.24  % [INFO] 	 nitpick registered as external prover. 
% 1.76/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.83/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.96/1.33  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.96/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.96/1.35  % [INFO] 	 Type checking passed. 
% 1.96/1.35  % [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 ... 
% 16.79/4.00  % [INFO] 	 Killing All external provers ... 
% 16.79/4.00  % Time passed: 3457ms (effective reasoning time: 2977ms)
% 16.79/4.00  % 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)>
% 16.79/4.00  % 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_2p_Osimps_I1_J, fact_1p_Osimps_I2_J
% 16.79/4.00  % No. of inferences in proof: 36
% 16.79/4.00  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3457 ms resp. 2977 ms w/o parsing
% 16.86/4.08  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.86/4.08  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------