TSTP Solution File: NUM686^1 by Leo-III---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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  7 08:00:30 EDT 2024

% Result   : Theorem 2.68s 1.60s
% Output   : Refutation 3.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   22 (   3 unt;   8 typ;   0 def)
%            Number of atoms       :   37 (   2 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   87 (   2   ~;   0   |;   0   &;  79   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   16 (   0   ^  16   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(x_type,type,
    x: nat ).

thf(y_type,type,
    y: nat ).

thf(z_type,type,
    z: nat ).

thf(u_type,type,
    u: nat ).

thf(some_type,type,
    some: ( nat > $o ) > $o ).

thf(diffprop_type,type,
    diffprop: nat > nat > nat > $o ).

thf(pl_type,type,
    pl: nat > nat > nat ).

thf(4,axiom,
    some @ ( diffprop @ z @ u ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).

thf(10,plain,
    some @ ( diffprop @ z @ u ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( some @ ( diffprop @ A @ B ) )
     => ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).

thf(14,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( some @ ( diffprop @ A @ B ) )
     => ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
    some @ ( diffprop @ x @ y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(9,plain,
    some @ ( diffprop @ x @ y ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: nat,B: nat] :
      ( ( pl @ A @ B )
      = ( pl @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).

thf(17,plain,
    ! [A: nat,B: nat] :
      ( ( pl @ A @ B )
      = ( pl @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( some @ ( diffprop @ B @ A ) )
     => ( ( some @ ( diffprop @ C @ B ) )
       => ( some @ ( diffprop @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).

thf(11,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( some @ ( diffprop @ B @ A ) )
     => ( ( some @ ( diffprop @ C @ B ) )
       => ( some @ ( diffprop @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).

thf(2,negated_conjecture,
    ~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(24,plain,
    $false,
    inference(e,[status(thm)],[10,14,9,17,11,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon May  6 12:27:24 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.85/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.24/0.96  % [INFO] 	 Parsing done (113ms). 
% 1.24/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.23  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.87/1.26  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.87/1.27  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.87/1.27  % [INFO] 	 Type checking passed. 
% 1.87/1.28  % [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 ... 
% 2.68/1.60  % External prover 'e' found a proof!
% 2.68/1.60  % [INFO] 	 Killing All external provers ... 
% 2.68/1.60  % Time passed: 1087ms (effective reasoning time: 631ms)
% 2.68/1.60  % 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)>
% 2.68/1.60  % Axioms used in derivation (5): n, m, satz15, satz19a, satz6
% 2.68/1.60  % No. of inferences in proof: 14
% 2.68/1.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1087 ms resp. 631 ms w/o parsing
% 3.07/1.67  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.07/1.67  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------