%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM730_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 01:36:04 EDT 2024

% Result   : Theorem 2.42s 1.65s
% Output   : Refutation 2.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   20 (   2 unt;  12 typ;   0 def)
%            Number of atoms       :   26 (   6 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :  117 (   3   ~;   0   |;   0   &; 114   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :    6 (   0   ^   6   !;   0   ?;   6   :)

% Comments : 
%------------------------------------------------------------------------------
thf(frac_type,type,
    frac: $tType ).

thf(x_type,type,
    x: frac ).

thf(y_type,type,
    y: frac ).

thf(orec3_type,type,
    orec3: $o > $o > $o > $o ).

thf(nat_type,type,
    nat: $tType ).

thf(ts_type,type,
    ts: nat > nat > nat ).

thf(c1x_type,type,
    c1x: frac > nat ).

thf(c2y_type,type,
    c2y: frac > nat ).

thf(c1y_type,type,
    c1y: frac > nat ).

thf(c2x_type,type,
    c2x: frac > nat ).

thf(more_type,type,
    more: nat > nat > $o ).

thf(less_type,type,
    less: nat > nat > $o ).

thf(1,conjecture,
    ( orec3
    @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
      = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
    @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
    @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41) ).

thf(2,negated_conjecture,
    ~ ( orec3
      @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
        = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ~ ( orec3
      @ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
        = ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
      @ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: nat,B: nat] : ( orec3 @ ( A = B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10) ).

thf(5,plain,
    ! [A: nat,B: nat] : ( orec3 @ ( A = B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,plain,
    ! [B: nat,A: nat] : ( orec3 @ ( A = B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(7,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[4,6]) ).

thf(8,plain,
    $false,
    inference(simp,[status(thm)],[7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM730_8 : TPTP v8.2.0. Released v8.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n028.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May 20 04:52:08 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.96/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.25/1.02  % [INFO] 	 Parsing done (130ms). 
% 1.25/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.30  % [INFO] 	 nitpick registered as external prover. 
% 1.60/1.31  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.92/1.40  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.92/1.41  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.92/1.41  % [INFO] 	 Type checking passed. 
% 1.92/1.42  % [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 ... 
% 2.42/1.65  % [INFO] 	 Killing All external provers ... 
% 2.42/1.65  % Time passed: 1128ms (effective reasoning time: 604ms)
% 2.42/1.65  % 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)>
% 2.42/1.65  % Axioms used in derivation (1): satz10
% 2.42/1.65  % No. of inferences in proof: 8
% 2.42/1.65  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1128 ms resp. 604 ms w/o parsing
% 2.42/1.68  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.42/1.68  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------