TSTP Solution File: NUM848+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM848+1 : TPTP v8.2.0. Released v4.1.0.
% 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 21 01:36:34 EDT 2024

% Result   : Theorem 53.61s 8.85s
% Output   : Refutation 53.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   20 (   9 unt;   7 typ;   0 def)
%            Number of atoms       :   17 (  16 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  138 (   7   ~;   1   |;   3   &; 127   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   11 (   0   ^  11   !;   0   ?;  11   :)

% Comments : 
%------------------------------------------------------------------------------
thf(vplus_type,type,
    vplus: $i > $i > $i ).

thf(vmul_type,type,
    vmul: $i > $i > $i ).

thf(vd436_type,type,
    vd436: $i ).

thf(vd437_type,type,
    vd437: $i ).

thf(vd439_type,type,
    vd439: $i ).

thf(vsucc_type,type,
    vsucc: $i > $i ).

thf(v1_type,type,
    v1: $i ).

thf(1,conjecture,
    ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) )
    = ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ ( vsucc @ vd439 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 4)') ).

thf(2,negated_conjecture,
    ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) )
   != ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ ( vsucc @ vd439 ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(59,plain,
    ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) )
   != ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ ( vsucc @ vd439 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(60,plain,
    ( ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vmul @ vd436 @ ( vsucc @ vd439 ) ) )
   != ( vplus @ ( vmul @ vd436 @ vd437 ) @ ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) ) ),
    inference(lifteq,[status(thm)],[59]) ).

thf(252,plain,
    ( ( ( vmul @ vd436 @ vd437 )
     != ( vmul @ vd436 @ vd437 ) )
    | ( ( vmul @ vd436 @ ( vsucc @ vd439 ) )
     != ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) ) ),
    inference(simp,[status(thm)],[60]) ).

thf(265,plain,
    ( ( vmul @ vd436 @ ( vsucc @ vd439 ) )
   != ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) ),
    inference(simp,[status(thm)],[252]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( vmul @ A @ ( vsucc @ B ) )
        = ( vplus @ ( vmul @ A @ B ) @ A ) )
      & ( ( vmul @ A @ v1 )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).

thf(161,plain,
    ! [A: $i,B: $i] :
      ( ( ( vmul @ A @ ( vsucc @ B ) )
        = ( vplus @ ( vmul @ A @ B ) @ A ) )
      & ( ( vmul @ A @ v1 )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(162,plain,
    ( ! [A: $i,B: $i] :
        ( ( vmul @ A @ ( vsucc @ B ) )
        = ( vplus @ ( vmul @ A @ B ) @ A ) )
    & ! [A: $i] :
        ( ( vmul @ A @ v1 )
        = A ) ),
    inference(miniscope,[status(thm)],[161]) ).

thf(164,plain,
    ! [B: $i,A: $i] :
      ( ( vmul @ A @ ( vsucc @ B ) )
      = ( vplus @ ( vmul @ A @ B ) @ A ) ),
    inference(cnf,[status(esa)],[162]) ).

thf(167,plain,
    ! [B: $i,A: $i] :
      ( ( vmul @ A @ ( vsucc @ B ) )
      = ( vplus @ ( vmul @ A @ B ) @ A ) ),
    inference(lifteq,[status(thm)],[164]) ).

thf(7901,plain,
    ( ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 )
   != ( vplus @ ( vmul @ vd436 @ vd439 ) @ vd436 ) ),
    inference(rewrite,[status(thm)],[265,167]) ).

thf(7902,plain,
    $false,
    inference(simp,[status(thm)],[7901]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM848+1 : TPTP v8.2.0. Released v4.1.0.
% 0.13/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 06:43:24 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.91/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.14  % [INFO] 	 Parsing done (205ms). 
% 1.28/1.15  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.43  % [INFO] 	 nitpick registered as external prover. 
% 1.83/1.44  % [INFO] 	 Scanning for conjecture ... 
% 2.10/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 56 axioms. Running axiom selection ... 
% 2.22/1.56  % [INFO] 	 Axiom selection finished. Selected 56 axioms (removed 0 axioms). 
% 2.51/1.64  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.51/1.65  % [INFO] 	 Type checking passed. 
% 2.51/1.65  % [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 ... 
% 53.61/8.84  % [INFO] 	 Killing All external provers ... 
% 53.61/8.85  % Time passed: 8347ms (effective reasoning time: 7691ms)
% 53.61/8.85  % 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)>
% 53.61/8.85  % Axioms used in derivation (1): qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))
% 53.61/8.85  % No. of inferences in proof: 13
% 53.61/8.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8347 ms resp. 7691 ms w/o parsing
% 53.61/8.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.61/8.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------