TSTP Solution File: SYO068^4.001 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% 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 08:59:11 EDT 2024

% Result   : Theorem 3.92s 2.26s
% Output   : Refutation 3.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   33 (  13 unt;   9 typ;   3 def)
%            Number of atoms       :   69 (   5 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  116 (  20   ~;  16   |;   0   &;  76   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :   33 (   3   ^  30   !;   0   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
thf(irel_type,type,
    irel: $i > $i > $o ).

thf(iatom_type,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(iatom_def,definition,
    ( iatom
    = ( ^ [A: $i > $o] : A ) ) ).

thf(iimplies_type,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(iimplies_def,definition,
    ( iimplies
    = ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).

thf(ivalid_type,type,
    ivalid: ( $i > $o ) > $o ).

thf(ivalid_def,definition,
    ( ivalid
    = ( '!' @ $i ) ) ).

thf(p0_type,type,
    p0: $i > $o ).

thf(p1_type,type,
    p1: $i > $o ).

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

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

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

thf(1,conjecture,
    ivalid @ ( iatom @ p0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( ivalid @ ( iatom @ p0 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ! [A: $i] : ( p0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    ~ ( p0 @ sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(3,axiom,
    ! [A: $i] : ( irel @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).

thf(9,plain,
    ! [A: $i] : ( irel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,plain,
    ! [A: $i] : ( irel @ A @ A ),
    inference(cnf,[status(esa)],[9]) ).

thf(6,axiom,
    ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).

thf(15,plain,
    ! [A: $i] :
      ( ~ ! [B: $i] :
            ( ( irel @ A @ B )
           => ( p1 @ B ) )
      | ! [B: $i] :
          ( ( irel @ A @ B )
         => ( ~ ! [C: $i] :
                  ( ( irel @ B @ C )
                 => ( p1 @ C ) )
            | ! [C: $i] :
                ( ( irel @ B @ C )
               => ( p0 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( p1 @ ( sk2 @ A ) )
      | ~ ( irel @ A @ B )
      | ~ ( p1 @ ( sk3 @ B @ A ) )
      | ~ ( irel @ B @ C )
      | ( p0 @ C ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(5,axiom,
    ivalid @ ( iatom @ p1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).

thf(13,plain,
    ! [A: $i] : ( p1 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,plain,
    ! [A: $i] : ( p1 @ A ),
    inference(cnf,[status(esa)],[13]) ).

thf(32,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ ( irel @ A @ B )
      | ~ $true
      | ~ ( irel @ B @ C )
      | ( p0 @ C ) ),
    inference(rewrite,[status(thm)],[19,14]) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( irel @ A @ B )
      | ~ ( irel @ B @ C )
      | ( p0 @ C ) ),
    inference(simp,[status(thm)],[32]) ).

thf(36,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( irel @ B @ C )
      | ( p0 @ D )
      | ( ( irel @ A @ A )
       != ( irel @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[10,33]) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ~ ( irel @ B @ A )
      | ( p0 @ A ) ),
    inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(47,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( p0 @ B )
      | ( ( irel @ A @ A )
       != ( irel @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10,37]) ).

thf(48,plain,
    ! [A: $i] : ( p0 @ A ),
    inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(51,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[8,48]) ).

thf(52,plain,
    $false,
    inference(simp,[status(thm)],[51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n008.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon May 20 10:41:39 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.90/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/1.12  % [INFO] 	 Parsing done (204ms). 
% 1.32/1.13  % [INFO] 	 Running in sequential loop mode. 
% 2.00/1.48  % [INFO] 	 nitpick registered as external prover. 
% 2.00/1.48  % [INFO] 	 Scanning for conjecture ... 
% 2.15/1.61  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.33/1.63  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.33/1.64  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.33/1.64  % [INFO] 	 Type checking passed. 
% 2.33/1.65  % [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 ... 
% 3.92/2.26  % [INFO] 	 Killing All external provers ... 
% 3.92/2.26  % Time passed: 1803ms (effective reasoning time: 1118ms)
% 3.92/2.26  % 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)>
% 3.92/2.26  % Axioms used in derivation (3): refl_axiom, axiom2, axiom1
% 3.92/2.26  % No. of inferences in proof: 21
% 3.92/2.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1803 ms resp. 1118 ms w/o parsing
% 3.92/2.32  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.92/2.32  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------