%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYN986+1.003 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 08:16:57 EDT 2024

% Result   : Theorem 3.53s 2.24s
% Output   : Refutation 3.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   11 (   3 unt;   3 typ;   0 def)
%            Number of atoms       :   21 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   79 (   2   ~;   0   |;   9   &;  64   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   2 con; 0-3 aty)
%            Number of variables   :   22 (   0   ^  10   !;  12   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
thf(r_type,type,
    r: $i > $i > $i > $o ).

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

thf(succ_type,type,
    succ: $i > $i ).

thf(1,conjecture,
    ? [A: $i,B: $i,C: $i,D: $i] :
      ( ( r @ zero @ zero @ A )
      & ( r @ zero @ A @ B )
      & ( r @ zero @ B @ C )
      & ( r @ zero @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ck) ).

thf(2,negated_conjecture,
    ~ ? [A: $i,B: $i,C: $i,D: $i] :
        ( ( r @ zero @ zero @ A )
        & ( r @ zero @ A @ B )
        & ( r @ zero @ B @ C )
        & ( r @ zero @ C @ D ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ? [A: $i,B: $i,C: $i,D: $i] :
        ( ( r @ zero @ zero @ A )
        & ( r @ zero @ A @ B )
        & ( r @ zero @ B @ C )
        & ( r @ zero @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i] : ( r @ A @ zero @ ( succ @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hyp1) ).

thf(8,plain,
    ! [A: $i] : ( r @ A @ zero @ ( succ @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r @ A @ B @ C )
     => ( ( r @ C @ B @ D )
       => ( r @ A @ ( succ @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hyp2) ).

thf(10,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r @ A @ B @ C )
     => ( ( r @ C @ B @ D )
       => ( r @ A @ ( succ @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(28,plain,
    $false,
    inference(e,[status(thm)],[5,8,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SYN986+1.003 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n012.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Mon May 20 14:05:54 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.01/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.09  % [INFO] 	 Parsing done (159ms). 
% 1.29/1.11  % [INFO] 	 Running in sequential loop mode. 
% 1.96/1.48  % [INFO] 	 eprover registered as external prover. 
% 1.96/1.49  % [INFO] 	 cvc4 registered as external prover. 
% 1.96/1.49  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.11/1.62  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.11/1.63  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.30/1.63  % [INFO] 	 Type checking passed. 
% 2.30/1.64  % [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 ... 
% 3.53/2.23  % External prover 'e' found a proof!
% 3.53/2.24  % [INFO] 	 Killing All external provers ... 
% 3.53/2.24  % Time passed: 1768ms (effective reasoning time: 1123ms)
% 3.53/2.24  % 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)>
% 3.53/2.24  % Axioms used in derivation (2): hyp1, hyp2
% 3.53/2.24  % No. of inferences in proof: 8
% 3.53/2.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1768 ms resp. 1123 ms w/o parsing
% 3.53/2.27  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.53/2.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------