TSTP Solution File: ALG176+1 by Leo-III---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : ALG176+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n018.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 : Mon Jun 24 04:01:01 EDT 2024

% Result   : Theorem 3.00s 1.95s
% Output   : Refutation 3.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   18 (   1 unt;   6 typ;   0 def)
%            Number of atoms       :   67 (  16 equ;   0 cnn)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  192 (  11   ~;   0   |;  16   &; 126   @)
%                                         (   0 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   40 (   0   ^  36   !;   4   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sorti1_type,type,
    sorti1: $i > $o ).

thf(sorti2_type,type,
    sorti2: $i > $o ).

thf(h_type,type,
    h: $i > $i ).

thf(j_type,type,
    j: $i > $i ).

thf(op1_type,type,
    op1: $i > $i > $i ).

thf(op2_type,type,
    op2: $i > $i > $i ).

thf(4,axiom,
    ! [A: $i] :
      ( ( sorti2 @ A )
     => ! [B: $i] :
          ( ( sorti2 @ B )
         => ( sorti2 @ ( op2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(25,plain,
    ! [A: $i] :
      ( ( sorti2 @ A )
     => ! [B: $i] :
          ( ( sorti2 @ B )
         => ( sorti2 @ ( op2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ? [A: $i] :
      ( ( sorti1 @ A )
      & ! [B: $i] :
          ( ( sorti1 @ B )
         => ( ( op1 @ B @ A )
           != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(27,plain,
    ? [A: $i] :
      ( ( sorti1 @ A )
      & ! [B: $i] :
          ( ( sorti1 @ B )
         => ( ( op1 @ B @ A )
           != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1,conjecture,
    ( ( ! [A: $i] :
          ( ( sorti1 @ A )
         => ( sorti2 @ ( h @ A ) ) )
      & ! [A: $i] :
          ( ( sorti2 @ A )
         => ( sorti1 @ ( j @ A ) ) ) )
   => ~ ( ! [A: $i] :
            ( ( sorti1 @ A )
           => ! [B: $i] :
                ( ( sorti1 @ B )
               => ( ( h @ ( op1 @ A @ B ) )
                  = ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
        & ! [A: $i] :
            ( ( sorti2 @ A )
           => ! [B: $i] :
                ( ( sorti2 @ B )
               => ( ( j @ ( op2 @ A @ B ) )
                  = ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
        & ! [A: $i] :
            ( ( sorti2 @ A )
           => ( ( h @ ( j @ A ) )
              = A ) )
        & ! [A: $i] :
            ( ( sorti1 @ A )
           => ( ( j @ ( h @ A ) )
              = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: $i] :
            ( ( sorti1 @ A )
           => ( sorti2 @ ( h @ A ) ) )
        & ! [A: $i] :
            ( ( sorti2 @ A )
           => ( sorti1 @ ( j @ A ) ) ) )
     => ~ ( ! [A: $i] :
              ( ( sorti1 @ A )
             => ! [B: $i] :
                  ( ( sorti1 @ B )
                 => ( ( h @ ( op1 @ A @ B ) )
                    = ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
          & ! [A: $i] :
              ( ( sorti2 @ A )
             => ! [B: $i] :
                  ( ( sorti2 @ B )
                 => ( ( j @ ( op2 @ A @ B ) )
                    = ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
          & ! [A: $i] :
              ( ( sorti2 @ A )
             => ( ( h @ ( j @ A ) )
                = A ) )
          & ! [A: $i] :
              ( ( sorti1 @ A )
             => ( ( j @ ( h @ A ) )
                = A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ( ( ! [A: $i] :
            ( ( sorti1 @ A )
           => ( sorti2 @ ( h @ A ) ) )
        & ! [A: $i] :
            ( ( sorti2 @ A )
           => ( sorti1 @ ( j @ A ) ) ) )
     => ~ ( ! [A: $i] :
              ( ( sorti1 @ A )
             => ! [B: $i] :
                  ( ( sorti1 @ B )
                 => ( ( h @ ( op1 @ A @ B ) )
                    = ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
          & ! [A: $i] :
              ( ( sorti2 @ A )
             => ! [B: $i] :
                  ( ( sorti2 @ B )
                 => ( ( j @ ( op2 @ A @ B ) )
                    = ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
          & ! [A: $i] :
              ( ( sorti2 @ A )
             => ( ( h @ ( j @ A ) )
                = A ) )
          & ! [A: $i] :
              ( ( sorti1 @ A )
             => ( ( j @ ( h @ A ) )
                = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ~ ? [A: $i] :
        ( ( sorti2 @ A )
        & ! [B: $i] :
            ( ( sorti2 @ B )
           => ( ( op2 @ B @ A )
             != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

thf(31,plain,
    ~ ? [A: $i] :
        ( ( sorti2 @ A )
        & ! [B: $i] :
            ( ( sorti2 @ B )
           => ( ( op2 @ B @ A )
             != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( sorti1 @ A )
     => ! [B: $i] :
          ( ( sorti1 @ B )
         => ( sorti1 @ ( op1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

thf(23,plain,
    ! [A: $i] :
      ( ( sorti1 @ A )
     => ! [B: $i] :
          ( ( sorti1 @ B )
         => ( sorti1 @ ( op1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(38,plain,
    $false,
    inference(e,[status(thm)],[25,27,7,31,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : ALG176+1 : TPTP v8.2.0. Released v2.7.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d THM
% 0.11/0.32  % Computer : n018.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Wed Jun 19 15:39:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.02/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/1.06  % [INFO] 	 Parsing done (116ms). 
% 1.20/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.35  % [INFO] 	 eprover registered as external prover. 
% 1.75/1.35  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.45  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.01/1.48  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.01/1.48  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.01/1.49  % [INFO] 	 Type checking passed. 
% 2.01/1.49  % [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 ... 
% 3.00/1.95  % External prover 'e' found a proof!
% 3.00/1.95  % [INFO] 	 Killing All external provers ... 
% 3.00/1.95  % Time passed: 1435ms (effective reasoning time: 873ms)
% 3.00/1.95  % 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)>
% 3.00/1.95  % Axioms used in derivation (4): ax2, ax3, ax4, ax1
% 3.00/1.95  % No. of inferences in proof: 12
% 3.00/1.95  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1435 ms resp. 873 ms w/o parsing
% 3.23/2.01  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.23/2.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------