TSTP Solution File: HEN010-3 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : HEN010-3 : TPTP v8.2.0. Released v1.0.0.
% 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 : Mon May 20 21:34:13 EDT 2024

% Result   : Unsatisfiable 2.73s 1.65s
% Output   : Refutation 2.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   22 (  11 unt;   5 typ;   0 def)
%            Number of atoms       :   25 (   8 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  102 (  10   ~;   8   |;   0   &;  84   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   26 (   0   ^  26   !;   0   ?;  26   :)

% Comments : 
%------------------------------------------------------------------------------
thf(divide_type,type,
    divide: $i > $i > $i ).

thf(identity_type,type,
    identity: $i ).

thf(a_type,type,
    a: $i ).

thf(less_equal_type,type,
    less_equal: $i > $i > $o ).

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

thf(8,axiom,
    ! [A: $i] : ( less_equal @ A @ identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).

thf(24,plain,
    ! [A: $i] : ( less_equal @ A @ identity ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [A: $i] : ( less_equal @ zero @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).

thf(20,plain,
    ! [A: $i] : ( less_equal @ zero @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_equal @ A @ B )
      | ~ ( less_equal @ B @ A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_equal @ A @ B )
      | ~ ( less_equal @ B @ A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,negated_conjecture,
    ( ( divide @ identity @ a )
   != ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).

thf(9,plain,
    ( ( divide @ identity @ a )
   != ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( less_equal @ A @ B )
      | ( ( divide @ A @ B )
        = zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ ( less_equal @ A @ B )
      | ( ( divide @ A @ B )
        = zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).

thf(18,plain,
    ! [B: $i,A: $i] : ( less_equal @ ( divide @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).

thf(19,plain,
    ! [C: $i,B: $i,A: $i] : ( less_equal @ ( divide @ ( divide @ A @ B ) @ ( divide @ C @ B ) ) @ ( divide @ ( divide @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( ( divide @ A @ B )
       != zero )
      | ( less_equal @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( ( divide @ A @ B )
       != zero )
      | ( less_equal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(26,plain,
    $false,
    inference(e,[status(thm)],[24,20,21,9,12,18,19,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : HEN010-3 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.12  % Command  : run_Leo-III %s %d
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sun May 19 22:49:08 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.79/0.79  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.11/0.90  % [INFO] 	 Parsing done (106ms). 
% 1.21/0.91  % [INFO] 	 Running in sequential loop mode. 
% 1.50/1.13  % [INFO] 	 eprover registered as external prover. 
% 1.50/1.13  % [INFO] 	 cvc4 registered as external prover. 
% 1.50/1.13  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.19  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 1.73/1.21  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.73/1.22  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.73/1.22  % [INFO] 	 Type checking passed. 
% 1.80/1.22  % [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 ... 
% 2.73/1.64  % External prover 'e' found a proof!
% 2.73/1.64  % [INFO] 	 Killing All external provers ... 
% 2.73/1.64  % Time passed: 1176ms (effective reasoning time: 733ms)
% 2.73/1.64  % Axioms used in derivation (7): identity_is_largest, quotient_less_equal2, less_equal_and_equal, zero_is_smallest, quotient_less_equal1, quotient_smaller_than_numerator, quotient_property
% 2.73/1.64  % No. of inferences in proof: 17
% 2.73/1.65  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1176 ms resp. 733 ms w/o parsing
% 2.73/1.68  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.73/1.68  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------