TSTP Solution File: SYO038-1.003.003 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYO038-1.003.003 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 12:34:59 EDT 2023

% Result   : Unsatisfiable 2.63s 1.53s
% Output   : Refutation 2.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   17 (  11 unt;   4 typ;   0 def)
%            Number of atoms       :   15 (   6 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   66 (   4   ~;   2   |;   0   &;  60   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 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(d_type,type,
    d: $i > $o ).

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

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

thf(one_type,type,
    one: $i ).

thf(2,axiom,
    ! [A: $i] :
      ( ( f @ A @ one )
      = ( s @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(9,plain,
    ! [A: $i] :
      ( ( f @ A @ one )
      = ( s @ one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( f @ ( s @ A ) @ ( s @ B ) )
      = ( f @ A @ ( f @ ( s @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( f @ ( s @ A ) @ ( s @ B ) )
      = ( f @ A @ ( f @ ( s @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(7,plain,
    ~ ( d @ ( f @ ( s @ ( s @ one ) ) @ ( s @ ( s @ one ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ~ ( d @ A )
      | ( d @ ( s @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

thf(16,plain,
    ! [A: $i] :
      ( ~ ( d @ A )
      | ( d @ ( s @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( f @ one @ ( s @ A ) )
      = ( s @ ( s @ ( f @ one @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(11,plain,
    ! [A: $i] :
      ( ( f @ one @ ( s @ A ) )
      = ( s @ ( s @ ( f @ one @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    d @ one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

thf(15,plain,
    d @ one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(23,plain,
    $false,
    inference(e,[status(thm)],[9,13,7,16,11,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem  : SYO038-1.003.003 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n019.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu May 18 18:45:58 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.83/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/0.94  % [INFO] 	 Parsing done (105ms). 
% 1.23/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.49/1.14  % [INFO] 	 eprover registered as external prover. 
% 1.49/1.14  % [INFO] 	 cvc4 registered as external prover. 
% 1.49/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.20  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.79/1.21  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.79/1.22  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.79/1.22  % [INFO] 	 Type checking passed. 
% 1.79/1.23  % [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 ... 
% 2.63/1.53  % External prover 'e' found a proof!
% 2.63/1.53  % [INFO] 	 Killing All external provers ... 
% 2.63/1.53  % Time passed: 1016ms (effective reasoning time: 579ms)
% 2.63/1.53  % 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)>
% 2.63/1.53  % Axioms used in derivation (5): ax4, ax1, ax2, ax3, ax5
% 2.63/1.53  % No. of inferences in proof: 13
% 2.63/1.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1016 ms resp. 579 ms w/o parsing
% 2.71/1.62  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.71/1.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------