TSTP Solution File: RNG001-3 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : RNG001-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 02:37:17 EDT 2024

% Result   : Unsatisfiable 4.44s 2.86s
% Output   : Refutation 4.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   23 (   9 unt;   6 typ;   0 def)
%            Number of atoms       :   45 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  196 (  30   ~;  28   |;   0   &; 138   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   60 (   0   ^  60   !;   0   ?;  60   :)

% Comments : 
%------------------------------------------------------------------------------
thf(product_type,type,
    product: $i > $i > $i > $o ).

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

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

thf(sum_type,type,
    sum: $i > $i > $i > $o ).

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

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

thf(8,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( sum @ C @ E @ G )
      | ( product @ A @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).

thf(20,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( sum @ C @ E @ G )
      | ( product @ A @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,negated_conjecture,
    ~ ( product @ a @ additive_identity @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).

thf(9,plain,
    ~ ( product @ a @ additive_identity @ additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(4,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ C @ D @ F )
      | ( sum @ A @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).

thf(13,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ C @ D @ F )
      | ( sum @ A @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(17,plain,
    ! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
    ! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).

thf(12,plain,
    ! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( product @ A @ F @ G )
      | ( sum @ C @ E @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).

thf(18,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ D @ E )
      | ~ ( sum @ B @ D @ F )
      | ~ ( product @ A @ F @ G )
      | ( sum @ C @ E @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(2,axiom,
    ! [A: $i] : ( sum @ additive_identity @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).

thf(11,plain,
    ! [A: $i] : ( sum @ additive_identity @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ A @ E @ F )
      | ( sum @ C @ D @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).

thf(15,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( sum @ A @ B @ C )
      | ~ ( sum @ B @ D @ E )
      | ~ ( sum @ A @ E @ F )
      | ( sum @ C @ D @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(25,plain,
    $false,
    inference(cvc4,[status(thm)],[20,9,13,17,12,18,11,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : RNG001-3 : TPTP v8.2.0. Released v1.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n016.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sat May 18 12:10:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.27/1.20  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.63/1.41  % [INFO] 	 Parsing done (204ms). 
% 1.63/1.42  % [INFO] 	 Running in sequential loop mode. 
% 2.29/1.92  % [INFO] 	 eprover registered as external prover. 
% 2.29/1.92  % [INFO] 	 cvc4 registered as external prover. 
% 2.45/1.93  % [INFO] 	 Scanning for conjecture ... 
% 2.57/2.03  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 2.71/2.07  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 2.71/2.09  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.71/2.10  % [INFO] 	 Type checking passed. 
% 2.71/2.10  % [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 ... 
% 4.44/2.85  % External prover 'cvc4' found a proof!
% 4.44/2.86  % [INFO] 	 Killing All external provers ... 
% 4.44/2.86  % Time passed: 2316ms (effective reasoning time: 1425ms)
% 4.44/2.86  % Axioms used in derivation (7): additive_identity1, closure_of_multiplication, associativity_of_addition2, distributivity2, associativity_of_addition1, additive_inverse1, distributivity1
% 4.44/2.86  % No. of inferences in proof: 17
% 4.44/2.86  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2316 ms resp. 1425 ms w/o parsing
% 4.55/2.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.55/2.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------