TSTP Solution File: BOO013-4 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 10:11:55 EDT 2023

% Result   : Unsatisfiable 2.71s 1.67s
% Output   : Refutation 2.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   30 (  23 unt;   7 typ;   0 def)
%            Number of atoms       :   23 (  22 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   88 (   2   ~;   0   |;   0   &;  86   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   28 (   0   ^;  28   !;   0   ?;  28   :)

% Comments : 
%------------------------------------------------------------------------------
thf(b_type,type,
    b: $i ).

thf(inverse_type,type,
    inverse: $i > $i ).

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

thf(add_type,type,
    add: $i > $i > $i ).

thf(multiply_type,type,
    multiply: $i > $i > $i ).

thf(additive_identity_type,type,
    additive_identity: $i ).

thf(multiplicative_identity_type,type,
    multiplicative_identity: $i ).

thf(7,axiom,
    ! [A: $i] :
      ( ( multiply @ A @ multiplicative_identity )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).

thf(25,plain,
    ! [A: $i] :
      ( ( multiply @ A @ multiplicative_identity )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( multiply @ A @ ( inverse @ A ) )
      = additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).

thf(29,plain,
    ! [A: $i] :
      ( ( multiply @ A @ ( inverse @ A ) )
      = additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( multiply @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( add @ A @ ( inverse @ A ) )
      = multiplicative_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).

thf(27,plain,
    ! [A: $i] :
      ( ( add @ A @ ( inverse @ A ) )
      = multiplicative_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,negated_conjecture,
    ( b
   != ( inverse @ a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).

thf(12,plain,
    ( b
   != ( inverse @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(10,axiom,
    ( ( add @ a @ b )
    = multiplicative_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_a_multiplicative_identity) ).

thf(31,plain,
    ( ( add @ a @ b )
    = multiplicative_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( add @ A @ additive_identity )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).

thf(23,plain,
    ! [A: $i] :
      ( ( add @ A @ additive_identity )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( add @ A @ ( multiply @ B @ C ) )
      = ( multiply @ ( add @ A @ B ) @ ( add @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).

thf(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( add @ A @ ( multiply @ B @ C ) )
      = ( multiply @ ( add @ A @ B ) @ ( add @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ( add @ A @ B )
      = ( add @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( add @ A @ B )
      = ( add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( add @ B @ C ) )
      = ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).

thf(21,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( add @ B @ C ) )
      = ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(11,axiom,
    ( ( multiply @ a @ b )
    = additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_an_additive_identity) ).

thf(33,plain,
    ( ( multiply @ a @ b )
    = additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(41,plain,
    $false,
    inference(e,[status(thm)],[25,29,17,27,12,31,23,19,15,21,33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% 0.08/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n021.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May 18 21:02:28 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.31/1.04  % [INFO] 	 Parsing done (127ms). 
% 1.31/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.30  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 1.94/1.31  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.94/1.33  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.94/1.33  % [INFO] 	 Type checking passed. 
% 1.94/1.33  % [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 ... 
% 2.71/1.67  % External prover 'e' found a proof!
% 2.71/1.67  % [INFO] 	 Killing All external provers ... 
% 2.71/1.67  % Time passed: 1140ms (effective reasoning time: 624ms)
% 2.71/1.67  % 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)>
% 2.71/1.67  % Axioms used in derivation (10): b_an_additive_identity, distributivity2, commutativity_of_multiply, multiplicative_inverse1, additive_id1, b_a_multiplicative_identity, commutativity_of_add, multiplicative_id1, additive_inverse1, distributivity1
% 2.71/1.67  % No. of inferences in proof: 23
% 2.71/1.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1140 ms resp. 624 ms w/o parsing
% 2.97/1.74  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.97/1.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------