TSTP Solution File: RNG009-7 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : RNG009-7 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 : Tue May 21 02:37:22 EDT 2024

% Result   : Unsatisfiable 3.80s 2.06s
% Output   : Refutation 4.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   32 (  25 unt;   7 typ;   0 def)
%            Number of atoms       :   25 (  24 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  118 (   2   ~;   0   |;   0   &; 116   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 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   :   38 (   0   ^  38   !;   0   ?;  38   :)

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

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

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

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

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

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

thf(additive_inverse_type,type,
    additive_inverse: $i > $i ).

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

thf(24,plain,
    ! [A: $i] :
      ( ( add @ A @ ( additive_inverse @ A ) )
      = additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(2,negated_conjecture,
    ( ( multiply @ b @ a )
   != c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).

thf(14,plain,
    ( ( multiply @ b @ a )
   != c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( add @ A @ additive_identity )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_identity) ).

thf(20,plain,
    ! [A: $i] :
      ( ( add @ A @ additive_identity )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( add @ A @ B )
      = ( add @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( add @ A @ B )
      = ( add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,negated_conjecture,
    ( ( multiply @ a @ b )
    = c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).

thf(13,plain,
    ( ( multiply @ a @ b )
    = c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( add @ ( additive_inverse @ A ) @ A )
      = additive_identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).

thf(22,plain,
    ! [A: $i] :
      ( ( add @ ( additive_inverse @ A ) @ A )
      = additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( add @ additive_identity @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).

thf(18,plain,
    ! [A: $i] :
      ( ( add @ additive_identity @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( add @ A @ ( add @ B @ C ) )
      = ( add @ ( add @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( add @ A @ ( add @ B @ C ) )
      = ( add @ ( add @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( add @ B @ C ) )
      = ( add @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).

thf(32,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)],[10]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ ( add @ A @ B ) @ C )
      = ( add @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ ( add @ A @ B ) @ C )
      = ( add @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( multiply @ A @ ( multiply @ A @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_x) ).

thf(36,plain,
    ! [A: $i] :
      ( ( multiply @ A @ ( multiply @ A @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ B @ C ) )
      = ( multiply @ ( multiply @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_multiplication) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( multiply @ A @ ( multiply @ B @ C ) )
      = ( multiply @ ( multiply @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(114,plain,
    $false,
    inference(e,[status(thm)],[24,14,20,28,13,22,18,26,32,34,36,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : RNG009-7 : TPTP v8.2.0. Released v1.0.0.
% 0.08/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n004.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sat May 18 12:24:39 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 1.00/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.35/1.04  % [INFO] 	 Parsing done (104ms). 
% 1.35/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.30  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.30  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.36  % [INFO] 	 Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ... 
% 2.04/1.38  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 2.04/1.40  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.04/1.40  % [INFO] 	 Type checking passed. 
% 2.04/1.40  % [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 ... 
% 3.80/2.05  % External prover 'e' found a proof!
% 3.80/2.05  % [INFO] 	 Killing All external provers ... 
% 3.80/2.06  % Time passed: 1502ms (effective reasoning time: 1002ms)
% 3.80/2.06  % Axioms used in derivation (10): x_cubed_is_x, commutativity_for_addition, associativity_for_addition, distribute2, left_additive_identity, associativity_for_multiplication, right_additive_identity, distribute1, right_additive_inverse, left_additive_inverse
% 3.80/2.06  % No. of inferences in proof: 25
% 3.80/2.06  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1502 ms resp. 1002 ms w/o parsing
% 4.11/2.08  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.11/2.08  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------