TSTP Solution File: LCL903+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 : Fri May 19 11:32:29 EDT 2023

% Result   : Theorem 3.64s 2.06s
% Output   : Refutation 3.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   35 (  18 unt;   5 typ;   0 def)
%            Number of atoms       :   48 (  15 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  170 (   2   ~;   0   |;   5   &; 150   @)
%                                         (   1 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   57 (   0   ^;  57   !;   0   ?;  57   :)

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

thf('\'0\'_type',type,
    '\'0\'': $i ).

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

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

thf('\'1\'_type',type,
    '\'1\'': $i ).

thf(6,axiom,
    ! [A: $i] : ( '\'>=\'' @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).

thf(28,plain,
    ! [A: $i] : ( '\'>=\'' @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( '\'+\'' @ A @ B )
      = ( '\'+\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).

thf(22,plain,
    ! [A: $i,B: $i] :
      ( ( '\'+\'' @ A @ B )
      = ( '\'+\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( '\'==>\'' @ ( '\'==>\'' @ ( '\'==>\'' @ A @ '\'1\'' ) @ A ) @ A )
      = '\'0\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).

thf(54,plain,
    ! [A: $i] :
      ( ( '\'==>\'' @ ( '\'==>\'' @ ( '\'==>\'' @ A @ '\'1\'' ) @ A ) @ A )
      = '\'0\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'>=\'' @ ( '\'+\'' @ A @ B ) @ C )
    <=> ( '\'>=\'' @ B @ ( '\'==>\'' @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).

thf(35,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( '\'>=\'' @ ( '\'+\'' @ A @ B ) @ C )
       => ( '\'>=\'' @ B @ ( '\'==>\'' @ A @ C ) ) )
      & ( ( '\'>=\'' @ B @ ( '\'==>\'' @ A @ C ) )
       => ( '\'>=\'' @ ( '\'+\'' @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'>=\'' @ A @ B )
     => ( '\'>=\'' @ ( '\'==>\'' @ C @ A ) @ ( '\'==>\'' @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).

thf(48,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'>=\'' @ A @ B )
     => ( '\'>=\'' @ ( '\'==>\'' @ C @ A ) @ ( '\'==>\'' @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( '\'+\'' @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( '\'+\'' @ A @ A )
        = A ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(16,plain,
    ~ ! [A: $i] :
        ( ( '\'+\'' @ A @ A )
        = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,axiom,
    ! [A: $i] : ( '\'>=\'' @ A @ '\'0\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).

thf(40,plain,
    ! [A: $i] : ( '\'>=\'' @ A @ '\'0\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'>=\'' @ A @ B )
     => ( '\'>=\'' @ ( '\'+\'' @ A @ C ) @ ( '\'+\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).

thf(42,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'>=\'' @ A @ B )
     => ( '\'>=\'' @ ( '\'+\'' @ A @ C ) @ ( '\'+\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( '\'+\'' @ A @ '\'0\'' )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).

thf(25,plain,
    ! [A: $i] :
      ( ( '\'+\'' @ A @ '\'0\'' )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( ( '\'>=\'' @ A @ B )
        & ( '\'>=\'' @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).

thf(32,plain,
    ! [A: $i,B: $i] :
      ( ( ( '\'>=\'' @ A @ B )
        & ( '\'>=\'' @ B @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'>=\'' @ A @ B )
     => ( '\'>=\'' @ ( '\'==>\'' @ B @ C ) @ ( '\'==>\'' @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).

thf(45,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'>=\'' @ A @ B )
     => ( '\'>=\'' @ ( '\'==>\'' @ B @ C ) @ ( '\'==>\'' @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( '\'>=\'' @ A @ B )
        & ( '\'>=\'' @ B @ C ) )
     => ( '\'>=\'' @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).

thf(30,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( '\'>=\'' @ A @ B )
        & ( '\'>=\'' @ B @ C ) )
     => ( '\'>=\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( '\'+\'' @ A @ '\'1\'' )
      = '\'1\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).

thf(51,plain,
    ! [A: $i] :
      ( ( '\'+\'' @ A @ '\'1\'' )
      = '\'1\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C )
      = ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).

thf(19,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C )
      = ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(107,plain,
    $false,
    inference(e,[status(thm)],[28,22,54,35,48,16,40,42,25,32,45,30,51,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem  : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% 0.08/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n026.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May 18 16:30:36 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.90/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/1.01  % [INFO] 	 Parsing done (141ms). 
% 1.22/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.66/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.66/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.32  % [INFO] 	 Found a conjecture and 13 axioms. Running axiom selection ... 
% 1.79/1.34  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 1.95/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.01/1.37  % [INFO] 	 Type checking passed. 
% 2.01/1.37  % [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 ... 
% 3.64/2.06  % External prover 'e' found a proof!
% 3.64/2.06  % [INFO] 	 Killing All external provers ... 
% 3.64/2.06  % Time passed: 1583ms (effective reasoning time: 1032ms)
% 3.64/2.06  % Solved by 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)>
% 3.64/2.06  % Axioms used in derivation (13): sos_01, sos_05, sos_02, sos_11, sos_07, sos_13, sos_08, sos_12, sos_06, sos_09, sos_03, sos_04, sos_10
% 3.64/2.06  % No. of inferences in proof: 30
% 3.64/2.06  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1583 ms resp. 1032 ms w/o parsing
% 3.64/2.11  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.64/2.11  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------