TSTP Solution File: LCL163-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LCL163-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 00:04:52 EDT 2024

% Result   : Unsatisfiable 3.13s 1.69s
% Output   : Refutation 3.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   37 (  29 unt;   8 typ;   0 def)
%            Number of atoms       :   29 (  28 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  146 (   2   ~;   0   |;   0   &; 144   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   38 (   0   ^  38   !;   0   ?;  38   :)

% Comments : 
%------------------------------------------------------------------------------
thf(implies_type,type,
    implies: $i > $i > $i ).

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

thf(y_type,type,
    y: $i ).

thf(not_type,type,
    not: $i > $i ).

thf(xor_type,type,
    xor: $i > $i > $i ).

thf(truth_type,type,
    truth: $i ).

thf(falsehood_type,type,
    falsehood: $i ).

thf(and_star_type,type,
    and_star: $i > $i > $i ).

thf(3,axiom,
    ! [A: $i] :
      ( ( xor @ A @ falsehood )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

thf(20,plain,
    ! [A: $i] :
      ( ( xor @ A @ falsehood )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( xor @ A @ A )
      = falsehood ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

thf(22,plain,
    ! [A: $i] :
      ( ( xor @ A @ A )
      = falsehood ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( not @ A )
      = ( xor @ A @ truth ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

thf(18,plain,
    ! [A: $i] :
      ( ( not @ A )
      = ( xor @ A @ truth ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1,negated_conjecture,
    ( ( implies @ ( implies @ x @ y ) @ y )
   != ( implies @ ( implies @ y @ x ) @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).

thf(15,plain,
    ( ( implies @ ( implies @ x @ y ) @ y )
   != ( implies @ ( implies @ y @ x ) @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ( implies @ A @ B )
      = ( xor @ truth @ ( and_star @ A @ ( xor @ truth @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).

thf(42,plain,
    ! [B: $i,A: $i] :
      ( ( implies @ A @ B )
      = ( xor @ truth @ ( and_star @ A @ ( xor @ truth @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( and_star @ A @ truth )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

thf(24,plain,
    ! [A: $i] :
      ( ( and_star @ A @ truth )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( and_star @ ( xor @ truth @ A ) @ A )
      = falsehood ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

thf(28,plain,
    ! [A: $i] :
      ( ( and_star @ ( xor @ truth @ A ) @ A )
      = falsehood ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ( and_star @ A @ B )
      = ( and_star @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ( ( and_star @ A @ B )
      = ( and_star @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ A ) @ B ) @ truth ) @ B )
      = ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ B ) @ A ) @ truth ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ A ) @ B ) @ truth ) @ B )
      = ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ B ) @ A ) @ truth ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( xor @ A @ B )
      = ( xor @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).

thf(34,plain,
    ! [B: $i,A: $i] :
      ( ( xor @ A @ B )
      = ( xor @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(13,axiom,
    ( ( not @ truth )
    = falsehood ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).

thf(40,plain,
    ( ( not @ truth )
    = falsehood ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( and_star @ A @ falsehood )
      = falsehood ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

thf(26,plain,
    ! [A: $i] :
      ( ( and_star @ A @ falsehood )
      = falsehood ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( and_star @ ( and_star @ A @ B ) @ C )
      = ( and_star @ A @ ( and_star @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_associativity) ).

thf(36,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( and_star @ ( and_star @ A @ B ) @ C )
      = ( and_star @ A @ ( and_star @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( xor @ A @ ( xor @ truth @ B ) )
      = ( xor @ ( xor @ A @ truth ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ( xor @ A @ ( xor @ truth @ B ) )
      = ( xor @ ( xor @ A @ truth ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(49,plain,
    $false,
    inference(cvc4,[status(thm)],[20,22,18,15,42,24,28,38,32,34,40,26,36,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL163-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n002.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 03:17:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 1.00/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.97  % [INFO] 	 Parsing done (104ms). 
% 1.20/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.48/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 1.89/1.25  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 1.89/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.89/1.27  % [INFO] 	 Type checking passed. 
% 1.89/1.27  % [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 ... 
% 2.89/1.68  % External prover 'cvc4' found a proof!
% 3.13/1.68  % [INFO] 	 Killing All external provers ... 
% 3.13/1.69  % Time passed: 1160ms (effective reasoning time: 708ms)
% 3.13/1.69  % Axioms used in derivation (13): axiom_7, axiom_6, axiom_3, axiom_1, axiom_8, axiom_5, xor_commutativity, axiom_4, axiom_2, and_star_commutativity, and_star_associativity, false_definition, implies_definition
% 3.13/1.69  % No. of inferences in proof: 29
% 3.13/1.69  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1160 ms resp. 708 ms w/o parsing
% 3.13/1.71  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.13/1.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------