TSTP Solution File: ANA133-1 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n027.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 Jun 24 04:16:41 EDT 2024

% Result   : Unsatisfiable 7.27s 2.67s
% Output   : Refutation 7.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   44 (  35 unt;   9 typ;   0 def)
%            Number of atoms       :   35 (  34 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  164 (   2   ~;   0   |;   0   &; 162   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   48 (   0   ^  48   !;   0   ?;  48   :)

% Comments : 
%------------------------------------------------------------------------------
thf(d_type,type,
    d: $i > $i ).

thf(times_type,type,
    times: $i > $i > $i ).

thf(x_type,type,
    x: $i ).

thf(cos_type,type,
    cos: $i > $i ).

thf('\'+\'_type',type,
    '\'+\'': $i > $i > $i ).

thf(zero_type,type,
    zero: $i ).

thf(minus_type,type,
    minus: $i > $i ).

thf(one_type,type,
    one: $i ).

thf(sin_type,type,
    sin: $i > $i ).

thf(6,axiom,
    ( ( d @ one )
    = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_one) ).

thf(29,plain,
    ( ( d @ one )
    = zero ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(41,plain,
    ! [B: $i,A: $i] :
      ( ( times @ A @ B )
      = ( times @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(14,axiom,
    ( ( d @ x )
    = one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_x) ).

thf(45,plain,
    ( ( d @ x )
    = one ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) )
      = ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associtivity_of_plus) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) )
      = ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( times @ zero @ A )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).

thf(49,plain,
    ! [A: $i] :
      ( ( times @ zero @ A )
      = zero ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(11,axiom,
    ( ( d @ zero )
    = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_zero) ).

thf(39,plain,
    ( ( d @ zero )
    = zero ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( d @ ( sin @ A ) )
      = ( times @ ( cos @ A ) @ ( d @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_sin) ).

thf(35,plain,
    ! [A: $i] :
      ( ( d @ ( sin @ A ) )
      = ( times @ ( cos @ A ) @ ( d @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ( d @ A )
     != ( times @ x @ ( cos @ x ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

thf(18,plain,
    ! [A: $i] :
      ( ( d @ A )
     != ( times @ x @ ( cos @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( d @ ( cos @ A ) )
      = ( minus @ ( times @ ( sin @ A ) @ ( d @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_cos) ).

thf(31,plain,
    ! [A: $i] :
      ( ( d @ ( cos @ A ) )
      = ( minus @ ( times @ ( sin @ A ) @ ( d @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( times @ one @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).

thf(43,plain,
    ! [A: $i] :
      ( ( times @ one @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( '\'+\'' @ A @ ( minus @ A ) )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus) ).

thf(23,plain,
    ! [A: $i] :
      ( ( '\'+\'' @ A @ ( minus @ A ) )
      = zero ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( d @ ( times @ A @ B ) )
      = ( '\'+\'' @ ( times @ A @ ( d @ B ) ) @ ( times @ B @ ( d @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_times) ).

thf(51,plain,
    ! [B: $i,A: $i] :
      ( ( d @ ( times @ A @ B ) )
      = ( '\'+\'' @ ( times @ A @ ( d @ B ) ) @ ( times @ B @ ( d @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ( d @ ( '\'+\'' @ A @ B ) )
      = ( '\'+\'' @ ( d @ A ) @ ( d @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_plus) ).

thf(47,plain,
    ! [B: $i,A: $i] :
      ( ( d @ ( '\'+\'' @ A @ B ) )
      = ( '\'+\'' @ ( d @ A ) @ ( d @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

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

thf(37,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( times @ A @ ( times @ B @ C ) )
      = ( times @ ( times @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( '\'+\'' @ A @ B )
      = ( '\'+\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ( '\'+\'' @ A @ B )
      = ( '\'+\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( '\'+\'' @ zero @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).

thf(21,plain,
    ! [A: $i] :
      ( ( '\'+\'' @ zero @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( times @ A @ ( '\'+\'' @ B @ C ) )
      = ( '\'+\'' @ ( times @ A @ B ) @ ( times @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( times @ A @ ( '\'+\'' @ B @ C ) )
      = ( '\'+\'' @ ( times @ A @ B ) @ ( times @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1056,plain,
    $false,
    inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 04:15:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.33/1.03  % [INFO] 	 Parsing done (119ms). 
% 1.33/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ... 
% 1.91/1.35  % [INFO] 	 Axiom selection finished. Selected 16 axioms (removed 0 axioms). 
% 1.91/1.36  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.11/1.36  % [INFO] 	 Type checking passed. 
% 2.11/1.37  % [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 ... 
% 7.27/2.66  % External prover 'e' found a proof!
% 7.27/2.67  % [INFO] 	 Killing All external provers ... 
% 7.27/2.67  % Time passed: 2137ms (effective reasoning time: 1621ms)
% 7.27/2.67  % Axioms used in derivation (16): commutativity_of_plus, minus, derivative_of_times, derivative_of_zero, commutativity_of_times, derivative_of_cos, derivative_of_x, times_zero, derivative_of_sin, derivative_of_plus, associtivity_of_plus, distributivity, plus_zero, derivative_of_one, associativity_of_times, times_one
% 7.27/2.67  % No. of inferences in proof: 35
% 7.27/2.67  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2137 ms resp. 1621 ms w/o parsing
% 7.67/2.69  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.67/2.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------