TSTP Solution File: SYO038^1.003.004 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO038^1.003.004 : TPTP v8.2.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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 08:55:31 EDT 2024

% Result   : Theorem 20.11s 4.61s
% Output   : Refutation 20.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   18 (  12 unt;   4 typ;   0 def)
%            Number of atoms       :   16 (   6 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   74 (   2   ~;   0   |;   0   &;  70   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   10 (   0   ^  10   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
thf(one_type,type,
    one: $i ).

thf(s_type,type,
    s: $i > $i ).

thf(f_type,type,
    f: $i > $i > $i ).

thf(d_type,type,
    d: $i > $o ).

thf(3,axiom,
    ! [A: $i] :
      ( ( f @ A @ one )
      = ( s @ one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

thf(9,plain,
    ! [A: $i] :
      ( ( f @ A @ one )
      = ( s @ one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( f @ one @ ( s @ A ) )
      = ( s @ ( s @ ( f @ one @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(12,plain,
    ! [A: $i] :
      ( ( f @ one @ ( s @ A ) )
      = ( s @ ( s @ ( f @ one @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    d @ one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

thf(18,plain,
    d @ one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1,conjecture,
    d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ ( s @ one ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ ( s @ one ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ ( s @ one ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( d @ A )
     => ( d @ ( s @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

thf(19,plain,
    ! [A: $i] :
      ( ( d @ A )
     => ( d @ ( s @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( f @ ( s @ A ) @ ( s @ B ) )
      = ( f @ A @ ( f @ ( s @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(15,plain,
    ! [A: $i,B: $i] :
      ( ( f @ ( s @ A ) @ ( s @ B ) )
      = ( f @ A @ ( f @ ( s @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(2825,plain,
    $false,
    inference(e,[status(thm)],[9,12,18,8,19,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : SYO038^1.003.004 : TPTP v8.2.0. Released v5.3.0.
% 0.04/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n029.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.31  % CPULimit : 300
% 0.15/0.31  % WCLimit  : 300
% 0.15/0.31  % DateTime : Mon May 20 10:18:24 EDT 2024
% 0.15/0.31  % CPUTime  : 
% 0.87/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.22/1.08  % [INFO] 	 Parsing done (158ms). 
% 1.28/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.44  % [INFO] 	 eprover registered as external prover. 
% 1.80/1.44  % [INFO] 	 cvc4 registered as external prover. 
% 1.80/1.45  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 1.97/1.55  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 2.05/1.57  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.05/1.57  % [INFO] 	 Type checking passed. 
% 2.05/1.58  % [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 ... 
% 20.11/4.60  % External prover 'e' found a proof!
% 20.11/4.60  % [INFO] 	 Killing All external provers ... 
% 20.11/4.61  % Time passed: 4152ms (effective reasoning time: 3509ms)
% 20.11/4.61  % 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)>
% 20.11/4.61  % Axioms used in derivation (5): ax4, ax1, ax2, ax3, ax5
% 20.11/4.61  % No. of inferences in proof: 14
% 20.11/4.61  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4152 ms resp. 3509 ms w/o parsing
% 20.11/4.63  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.11/4.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------