TSTP Solution File: LDA007-2 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LDA007-2 : TPTP v8.1.2. Bugfixed v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n001.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 : Fri May 19 11:34:20 EDT 2023

% Result   : Unsatisfiable 3.04s 1.64s
% Output   : Refutation 3.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   57 (  31 unt;  16 typ;   0 def)
%            Number of atoms       :   51 (  36 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  186 (  10   ~;  10   |;   0   &; 166   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;  13 con; 0-2 aty)
%            Number of variables   :   42 (   0   ^;  42   !;   0   ?;  42   :)

% Comments : 
%------------------------------------------------------------------------------
thf(f_type,type,
    f: $i > $i > $i ).

thf(t_type,type,
    t: $i ).

thf(tsk_type,type,
    tsk: $i ).

thf(tt_ts_type,type,
    tt_ts: $i ).

thf(tk_type,type,
    tk: $i ).

thf(less_type,type,
    less: $i > $i > $o ).

thf(a_type,type,
    a: $i > $i > $i ).

thf(critical_point_type,type,
    critical_point: $i > $i ).

thf(k_type,type,
    k: $i ).

thf(ts_type,type,
    ts: $i ).

thf(sk_type,type,
    sk: $i ).

thf(s_type,type,
    s: $i ).

thf(ttk_type,type,
    ttk: $i ).

thf(tt_type,type,
    tt: $i ).

thf(stk_type,type,
    stk: $i ).

thf(st_type,type,
    st: $i ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( f @ A @ ( f @ B @ C ) )
      = ( f @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).

thf(56,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f @ A @ ( f @ B @ C ) )
      = ( f @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(15,axiom,
    ( ts
    = ( f @ t @ s ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).

thf(52,plain,
    ( ts
    = ( f @ t @ s ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(19,axiom,
    ( stk
    = ( f @ st @ k ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).

thf(61,plain,
    ( stk
    = ( f @ st @ k ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( less @ A @ ( critical_point @ B ) )
      | ( less @ A @ ( a @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).

thf(34,plain,
    ! [B: $i,A: $i] :
      ( ( less @ A @ ( critical_point @ B ) )
      | ( less @ A @ ( a @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,axiom,
    ( sk
    = ( f @ s @ k ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).

thf(44,plain,
    ( sk
    = ( f @ s @ k ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(16,axiom,
    ( tk
    = ( f @ t @ k ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).

thf(54,plain,
    ( tk
    = ( f @ t @ k ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(18,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( a @ A @ B )
       != B )
      | ( ( a @ ( f @ C @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).

thf(58,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( a @ A @ B )
       != B )
      | ( ( a @ ( f @ C @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( critical_point @ ( f @ A @ B ) )
      = ( a @ A @ ( critical_point @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ( critical_point @ ( f @ A @ B ) )
      = ( a @ A @ ( critical_point @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( a @ A @ ( a @ B @ C ) )
      = ( a @ ( f @ A @ B ) @ ( a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1a) ).

thf(42,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a @ A @ ( a @ B @ C ) )
      = ( a @ ( f @ A @ B ) @ ( a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(2,axiom,
    ! [A: $i] :
      ~ ( less @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).

thf(24,plain,
    ! [A: $i] :
      ~ ( less @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,axiom,
    ( ttk
    = ( f @ tt @ k ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).

thf(46,plain,
    ( ttk
    = ( f @ tt @ k ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less @ A @ B )
      | ( less @ ( a @ C @ A ) @ ( a @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( less @ A @ B )
      | ( less @ ( a @ C @ A ) @ ( a @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ( k
    = ( critical_point @ t ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).

thf(38,plain,
    ( k
    = ( critical_point @ t ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,negated_conjecture,
    ( ( f @ t @ tsk )
   != ( f @ tt_ts @ tk ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).

thf(21,plain,
    ( ( f @ t @ tsk )
   != ( f @ tt_ts @ tk ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(13,axiom,
    ( tt
    = ( f @ t @ t ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).

thf(48,plain,
    ( tt
    = ( f @ t @ t ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(20,axiom,
    ( st
    = ( f @ s @ t ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).

thf(63,plain,
    ( st
    = ( f @ s @ t ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(14,axiom,
    ( tt_ts
    = ( f @ tt @ ts ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).

thf(50,plain,
    ( tt_ts
    = ( f @ tt @ ts ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less @ A @ ( critical_point @ B ) )
      | ( ( a @ B @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less @ A @ ( critical_point @ B ) )
      | ( ( a @ B @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ( tsk
    = ( f @ ts @ k ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).

thf(40,plain,
    ( tsk
    = ( f @ ts @ k ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( a @ B @ A ) )
      | ( less @ A @ ( a @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( a @ B @ A ) )
      | ( less @ A @ ( a @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(83,plain,
    $false,
    inference(e,[status(thm)],[56,52,61,34,44,54,58,36,42,24,46,29,38,21,48,63,50,31,40,26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : LDA007-2 : TPTP v8.1.2. Bugfixed v2.6.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May 18 20:49:51 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.85/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/0.94  % [INFO] 	 Parsing done (111ms). 
% 1.22/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.50/1.15  % [INFO] 	 eprover registered as external prover. 
% 1.50/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.50/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.21  % [INFO] 	 Found a conjecture and 19 axioms. Running axiom selection ... 
% 1.89/1.25  % [INFO] 	 Axiom selection finished. Selected 19 axioms (removed 0 axioms). 
% 1.89/1.27  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.89/1.27  % [INFO] 	 Type checking passed. 
% 1.89/1.27  % [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 ... 
% 3.04/1.63  % External prover 'e' found a proof!
% 3.04/1.63  % [INFO] 	 Killing All external provers ... 
% 3.04/1.64  % Time passed: 1128ms (effective reasoning time: 680ms)
% 3.04/1.64  % 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)>
% 3.04/1.64  % Axioms used in derivation (19): clause_2, clause_1, clause_8, b4, clause_9, clause_6, a1, clause_3, a2, c3, clause_5, a1a, c2, b1, c1, clause_7, clause_10, clause_4, d2
% 3.04/1.64  % No. of inferences in proof: 41
% 3.04/1.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1128 ms resp. 680 ms w/o parsing
% 3.22/1.71  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.22/1.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------