TSTP Solution File: GRP700-10 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : GRP700-10 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 : Mon May 20 21:02:32 EDT 2024

% Result   : Unsatisfiable 3.20s 2.08s
% Output   : Refutation 3.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   25 (  19 unt;   6 typ;   0 def)
%            Number of atoms       :   19 (  18 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  122 (   2   ~;   0   |;   0   &; 120   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (   0   ^  34   !;   0   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tuple_type,type,
    tuple: $i > $i > $i ).

thf(mult_type,type,
    mult: $i > $i > $i ).

thf(x0_type,type,
    x0: $i ).

thf(unit_type,type,
    unit: $i ).

thf(ld_type,type,
    ld: $i > $i > $i ).

thf(rd_type,type,
    rd: $i > $i > $i ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ( tuple @ ( mult @ A @ x0 ) @ ( mult @ x0 @ A ) )
     != ( tuple @ unit @ unit ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).

thf(10,plain,
    ! [A: $i] :
      ( ( tuple @ ( mult @ A @ x0 ) @ ( mult @ x0 @ A ) )
     != ( tuple @ unit @ unit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) )
      = ( mult @ A @ ( mult @ ( mult @ ( mult @ B @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ ( mult @ A @ C ) )
      = ( mult @ A @ ( mult @ ( mult @ ( mult @ B @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

thf(21,plain,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ( mult @ A @ ( ld @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ A @ ( ld @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( mult @ ( rd @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ ( rd @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ B ) @ ( mult @ B @ ( mult @ C @ B ) ) )
      = ( mult @ ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ A @ B ) @ ( mult @ B @ ( mult @ C @ B ) ) )
      = ( mult @ ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).

thf(23,plain,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( rd @ ( mult @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

thf(19,plain,
    ! [B: $i,A: $i] :
      ( ( rd @ ( mult @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( ld @ A @ ( mult @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( ld @ A @ ( mult @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(33,plain,
    $false,
    inference(e,[status(thm)],[10,25,21,13,17,27,23,19,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : GRP700-10 : TPTP v8.2.0. Released v8.1.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n020.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sun May 19 05:29:24 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.91/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/1.05  % [INFO] 	 Parsing done (146ms). 
% 1.19/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.40  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.40  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.41  % [INFO] 	 Scanning for conjecture ... 
% 1.89/1.48  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 1.94/1.52  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.03/1.53  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.03/1.54  % [INFO] 	 Type checking passed. 
% 2.03/1.54  % [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 ... 
% 3.20/2.08  % External prover 'e' found a proof!
% 3.20/2.08  % [INFO] 	 Killing All external provers ... 
% 3.20/2.08  % Time passed: 1634ms (effective reasoning time: 1010ms)
% 3.20/2.08  % Axioms used in derivation (8): f08, f03, f02, f07, f06, f05, f04, f01
% 3.20/2.08  % No. of inferences in proof: 19
% 3.20/2.08  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1634 ms resp. 1010 ms w/o parsing
% 3.31/2.12  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.31/2.12  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------