TSTP Solution File: NUM415^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NUM415^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 01:29:46 EDT 2024

% Result   : Theorem 2.38s 1.47s
% Output   : Refutation 2.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   18 (  11 unt;   7 typ;   7 def)
%            Number of atoms       :   11 (   9 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   45 (   2   ~;   0   |;   0   &;  43   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   56 (  56   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   2 con; 0-4 aty)
%            Number of variables   :   16 (  16   ^   0   !;   0   ?;  16   :)

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

thf(one_def,definition,
    ( one
    = ( ^ [A: $i > $i] : A ) ) ).

thf(two_type,type,
    two: ( $i > $i ) > $i > $i ).

thf(two_def,definition,
    ( two
    = ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ B ) ) ) ) ).

thf(three_type,type,
    three: ( $i > $i ) > $i > $i ).

thf(three_def,definition,
    ( three
    = ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ B ) ) ) ) ) ).

thf(five_type,type,
    five: ( $i > $i ) > $i > $i ).

thf(five_def,definition,
    ( five
    = ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ).

thf(seven_type,type,
    seven: ( $i > $i ) > $i > $i ).

thf(seven_def,definition,
    ( seven
    = ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ) ) ).

thf(plus_type,type,
    plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(plus_def,definition,
    ( plus
    = ( ^ [A: ( $i > $i ) > $i > $i,B: ( $i > $i ) > $i > $i,C: $i > $i,D: $i] : ( A @ C @ ( B @ C @ D ) ) ) ) ).

thf(mult_type,type,
    mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(mult_def,definition,
    ( mult
    = ( ^ [A: ( $i > $i ) > $i > $i,B: ( $i > $i ) > $i > $i,C: $i > $i] : ( A @ ( B @ C ) ) ) ) ).

thf(1,conjecture,
    ( ( mult @ two @ ( plus @ three @ seven ) )
    = ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ( ( mult @ two @ ( plus @ three @ seven ) )
   != ( mult @ ( mult @ two @ five ) @ ( plus @ one @ one ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    $false,
    inference(simp,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM415^1 : TPTP v8.2.0. Released v3.6.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n003.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 : Mon May 20 06:27:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.98/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/1.06  % [INFO] 	 Parsing done (132ms). 
% 1.32/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.77/1.28  % [INFO] 	 eprover registered as external prover. 
% 1.77/1.28  % [INFO] 	 cvc4 registered as external prover. 
% 1.77/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.96/1.36  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.14/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.14/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.14/1.38  % [INFO] 	 Type checking passed. 
% 2.14/1.38  % [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 ... 
% 2.38/1.47  % [INFO] 	 Killing All external provers ... 
% 2.38/1.47  % Time passed: 939ms (effective reasoning time: 402ms)
% 2.38/1.47  % 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)>
% 2.38/1.47  % Axioms used in derivation (0): 
% 2.38/1.47  % No. of inferences in proof: 4
% 2.38/1.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 939 ms resp. 402 ms w/o parsing
% 2.45/1.51  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.45/1.51  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------