TSTP Solution File: SYN066+1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 11:00:59 EDT 2024

% Result   : Theorem 3.82s 1.83s
% Output   : Refutation 3.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   30 (  13 unt;   7 typ;   0 def)
%            Number of atoms       :   47 (   4 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  162 (  10   ~;   6   |;   4   &; 136   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   57 (   0   ^  44   !;  13   ?;  57   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_r_type,type,
    big_r: $i > $i > $o ).

thf(big_p_type,type,
    big_p: $i > $i > $o ).

thf(big_q_type,type,
    big_q: $i > $i > $o ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i > $i ).

thf(sk3_type,type,
    sk3: $i > $i > $i ).

thf(sk4_type,type,
    sk4: $i > $i > $i ).

thf(3,axiom,
    ! [A: $i] :
    ? [B: $i] :
    ! [C: $i] :
    ? [D: $i] :
      ( ( ( big_p @ C @ A )
       => ( big_p @ D @ B ) )
      & ( big_p @ D @ A )
      & ( ( big_p @ D @ B )
       => ? [E: $i] : ( big_q @ E @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel37_1) ).

thf(8,plain,
    ! [A: $i] :
    ? [B: $i] :
    ! [C: $i] :
    ? [D: $i] :
      ( ( ( big_p @ C @ A )
       => ( big_p @ D @ B ) )
      & ( big_p @ D @ A )
      & ( ( big_p @ D @ B )
       => ? [E: $i] : ( big_q @ E @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] : ( big_p @ ( sk3 @ B @ A ) @ A ),
    inference(cnf,[status(esa)],[8]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_p @ B @ A )
      | ( big_p @ ( sk3 @ B @ A ) @ ( sk2 @ A ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(20,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_p @ ( sk3 @ D @ C ) @ ( sk2 @ C ) )
      | ( ( big_p @ ( sk3 @ B @ A ) @ A )
       != ( big_p @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[10,11]) ).

thf(21,plain,
    ! [B: $i,A: $i] : ( big_p @ ( sk3 @ ( sk3 @ A @ B ) @ B ) @ ( sk2 @ B ) ),
    inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sk3 @ E @ F ))]]) ).

thf(24,plain,
    ! [B: $i,A: $i] : ( big_p @ ( sk3 @ ( sk3 @ A @ B ) @ B ) @ ( sk2 @ B ) ),
    inference(simp,[status(thm)],[21]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( big_p @ ( sk3 @ B @ A ) @ ( sk2 @ A ) )
      | ( big_q @ ( sk4 @ B @ A ) @ ( sk2 @ A ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(40,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( big_q @ ( sk4 @ D @ C ) @ ( sk2 @ C ) )
      | ( ( big_p @ ( sk3 @ ( sk3 @ A @ B ) @ B ) @ ( sk2 @ B ) )
       != ( big_p @ ( sk3 @ D @ C ) @ ( sk2 @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,9]) ).

thf(41,plain,
    ! [B: $i,A: $i] : ( big_q @ ( sk4 @ ( sk3 @ A @ B ) @ B ) @ ( sk2 @ B ) ),
    inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( sk3 @ E @ F ))]]) ).

thf(44,plain,
    ! [B: $i,A: $i] : ( big_q @ ( sk4 @ ( sk3 @ A @ B ) @ B ) @ ( sk2 @ B ) ),
    inference(simp,[status(thm)],[41]) ).

thf(5,axiom,
    ( ? [A: $i,B: $i] : ( big_q @ A @ B )
   => ! [A: $i] : ( big_r @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel37_3) ).

thf(14,plain,
    ( ? [A: $i,B: $i] : ( big_q @ A @ B )
   => ! [A: $i] : ( big_r @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( big_q @ A @ B )
      | ( big_r @ C @ C ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(46,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( big_r @ E @ E )
      | ( ( big_q @ ( sk4 @ ( sk3 @ A @ B ) @ B ) @ ( sk2 @ B ) )
       != ( big_q @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[44,15]) ).

thf(47,plain,
    ! [A: $i] : ( big_r @ A @ A ),
    inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( sk4 @ ( sk3 @ H @ J ) @ J )),bind(D,$thf( sk2 @ J )),bind(E,$thf( E ))]]) ).

thf(48,plain,
    ! [A: $i] : ( big_r @ A @ A ),
    inference(simp,[status(thm)],[47]) ).

thf(1,conjecture,
    ! [A: $i] :
    ? [B: $i] : ( big_r @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel37) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
      ? [B: $i] : ( big_r @ A @ B ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: $i] :
      ? [B: $i] : ( big_r @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ! [A: $i] :
      ~ ( big_r @ sk1 @ A ),
    inference(cnf,[status(esa)],[6]) ).

thf(69,plain,
    ! [B: $i,A: $i] :
      ( ( big_r @ A @ A )
     != ( big_r @ sk1 @ B ) ),
    inference(paramod_ordered,[status(thm)],[48,7]) ).

thf(70,plain,
    $false,
    inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n025.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May  6 21:15:54 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.92/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.16/0.97  % [INFO] 	 Parsing done (113ms). 
% 1.24/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.67/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.24  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.87/1.26  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.87/1.26  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.87/1.27  % [INFO] 	 Type checking passed. 
% 1.87/1.27  % [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 ... 
% 3.82/1.83  % [INFO] 	 Killing All external provers ... 
% 3.82/1.83  % Time passed: 1302ms (effective reasoning time: 852ms)
% 3.82/1.83  % 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)>
% 3.82/1.83  % Axioms used in derivation (2): pel37_1, pel37_3
% 3.82/1.83  % No. of inferences in proof: 23
% 3.82/1.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1302 ms resp. 852 ms w/o parsing
% 3.82/1.87  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.82/1.87  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------