%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : ROB005-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : Fri May 19 11:49:55 EDT 2023

% Result   : Unsatisfiable 22.31s 4.47s
% Output   : Refutation 22.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   16 (  11 unt;   5 typ;   0 def)
%            Number of atoms       :   11 (  10 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   72 (   2   ~;   0   |;   0   &;  70   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^;  14   !;   0   ?;  14   :)

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

thf(negate_type,type,
    negate: $i > $i ).

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

thf(b_type,type,
    b: $i ).

thf(c_type,type,
    c: $i ).

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

thf(6,plain,
    ( ( add @ ( negate @ ( add @ a @ ( negate @ b ) ) ) @ ( negate @ ( add @ ( negate @ a ) @ ( negate @ b ) ) ) )
   != b ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( add @ A @ B )
      = ( add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( negate @ ( add @ ( negate @ ( add @ A @ B ) ) @ ( negate @ ( add @ A @ ( negate @ B ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(11,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( add @ ( add @ A @ B ) @ C )
      = ( add @ A @ ( add @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ( ( add @ c @ c )
    = c ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).

thf(15,plain,
    ( ( add @ c @ c )
    = c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8097,plain,
    $false,
    inference(e,[status(thm)],[6,9,13,11,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : ROB005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.29  % Computer : n032.cluster.edu
% 0.11/0.29  % Model    : x86_64 x86_64
% 0.11/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29  % Memory   : 8042.1875MB
% 0.11/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29  % CPULimit : 300
% 0.11/0.29  % WCLimit  : 300
% 0.11/0.29  % DateTime : Thu May 18 23:46:36 EDT 2023
% 0.11/0.29  % CPUTime  : 
% 0.72/0.72  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.82/0.84  % [INFO] 	 Parsing done (118ms). 
% 0.82/0.85  % [INFO] 	 Running in sequential loop mode. 
% 1.24/1.05  % [INFO] 	 eprover registered as external prover. 
% 1.24/1.05  % [INFO] 	 cvc4 registered as external prover. 
% 1.24/1.05  % [INFO] 	 Scanning for conjecture ... 
% 1.45/1.10  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.45/1.11  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.45/1.12  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.45/1.12  % [INFO] 	 Type checking passed. 
% 1.45/1.12  % [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 ... 
% 22.31/4.46  % External prover 'e' found a proof!
% 22.31/4.46  % [INFO] 	 Killing All external provers ... 
% 22.31/4.47  % Time passed: 4052ms (effective reasoning time: 3610ms)
% 22.31/4.47  % 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)>
% 22.31/4.47  % Axioms used in derivation (4): commutativity_of_add, robbins_axiom, associativity_of_add, idempotence
% 22.31/4.47  % No. of inferences in proof: 11
% 22.31/4.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4052 ms resp. 3610 ms w/o parsing
% 22.31/4.48  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.31/4.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------