TSTP Solution File: GRP401-1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP401-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 11:13:54 EDT 2023

% Result   : Unsatisfiable 42.68s 7.26s
% Output   : Refutation 42.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   18 (   9 unt;   5 typ;   0 def)
%            Number of atoms       :   17 (  16 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   94 (   6   ~;   4   |;   0   &;  84   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   28 (   0   ^;  28   !;   0   ?;  28   :)

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

thf(commutator_type,type,
    commutator: $i > $i > $i ).

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

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

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

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

thf(10,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ ( multiply @ A @ B ) @ C )
      = ( multiply @ A @ ( multiply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( multiply @ B @ ( multiply @ A @ ( commutator @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( commutator @ ( multiply @ A @ B ) @ C )
      = ( multiply @ ( commutator @ A @ C ) @ ( commutator @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator_distributes_over_product) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( commutator @ ( multiply @ A @ B ) @ C )
      = ( multiply @ ( commutator @ A @ C ) @ ( commutator @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(12,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( multiply @ A @ B )
       != ( multiply @ C @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ( ( multiply @ ( commutator @ a @ b ) @ c )
   != ( multiply @ c @ ( commutator @ a @ b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_nilpotency) ).

thf(7,plain,
    ( ( multiply @ ( commutator @ a @ b ) @ c )
   != ( multiply @ c @ ( commutator @ a @ b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

thf(16,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( multiply @ A @ B )
       != ( multiply @ A @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12939,plain,
    $false,
    inference(e,[status(thm)],[10,20,22,12,7,16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP401-1 : TPTP v8.1.2. Released v2.5.0.
% 0.16/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n007.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 : Fri May 19 01:55:24 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 1.00/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.26/0.98  % [INFO] 	 Parsing done (117ms). 
% 1.26/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.22  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.88/1.24  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.88/1.25  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.94/1.25  % [INFO] 	 Type checking passed. 
% 1.94/1.26  % [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 ... 
% 42.68/7.26  % External prover 'e' found a proof!
% 42.68/7.26  % [INFO] 	 Killing All external provers ... 
% 42.68/7.26  % Time passed: 6723ms (effective reasoning time: 6273ms)
% 42.68/7.26  % 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)>
% 42.68/7.26  % Axioms used in derivation (5): left_cancellation, right_cancellation, commutator, commutator_distributes_over_product, associativity_of_multiply
% 42.68/7.26  % No. of inferences in proof: 13
% 42.68/7.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6723 ms resp. 6273 ms w/o parsing
% 42.68/7.28  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.68/7.28  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------