%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : GRP660-11 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n032.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 07:07:38 EDT 2024

% Result   : Unsatisfiable 3.98s 1.99s
% Output   : Refutation 4.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   18 (  13 unt;   5 typ;   0 def)
%            Number of atoms       :   13 (  12 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   66 (   2   ~;   0   |;   0   &;  64   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   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   :   22 (   0   ^  22   !;   0   ?;  22   :)

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

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

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

thf(x1_type,type,
    x1: $i ).

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

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

thf(10,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/sandbox/benchmark/theBenchmark.p',f03) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ( mult @ ( rd @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ( ld @ A @ ( mult @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ( ( mult @ x0 @ ( rd @ x1 @ x1 ) )
   != x0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

thf(7,plain,
    ( ( mult @ x0 @ ( rd @ x1 @ x1 ) )
   != x0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

thf(18,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A )
      = ( mult @ A @ ( mult @ B @ ( mult @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( rd @ ( mult @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(308,plain,
    $false,
    inference(e,[status(thm)],[10,14,12,7,18,16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : GRP660-11 : TPTP v8.2.0. Released v8.1.0.
% 0.02/0.09  % Command  : run_Leo-III %s %d THM
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Thu Jun 20 10:41:55 EDT 2024
% 0.08/0.28  % CPUTime  : 
% 0.76/0.74  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.84/0.85  % [INFO] 	 Parsing done (108ms). 
% 1.02/0.85  % [INFO] 	 Running in sequential loop mode. 
% 1.24/1.07  % [INFO] 	 eprover registered as external prover. 
% 1.24/1.07  % [INFO] 	 Scanning for conjecture ... 
% 1.40/1.12  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 1.40/1.14  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.40/1.15  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.40/1.15  % [INFO] 	 Type checking passed. 
% 1.40/1.16  % [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 ... 
% 3.98/1.99  % External prover 'e' found a proof!
% 3.98/1.99  % [INFO] 	 Killing All external provers ... 
% 3.98/1.99  % Time passed: 1581ms (effective reasoning time: 1131ms)
% 3.98/1.99  % Axioms used in derivation (5): f03, f02, f05, f04, f01
% 3.98/1.99  % No. of inferences in proof: 13
% 3.98/1.99  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1581 ms resp. 1131 ms w/o parsing
% 4.42/2.01  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.42/2.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------