TSTP Solution File: SEV045^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEV045^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 04:10:49 EDT 2024

% Result   : Theorem 9.10s 2.74s
% Output   : Refutation 9.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   55 (  12 unt;   8 typ;   0 def)
%            Number of atoms       :  196 (  23 equ;   0 cnn)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives :  615 (  62   ~;  49   |;  15   &; 450   @)
%                                         (   0 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :  115 (   0   ^ 115   !;   0   ?; 115   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(b_type,type,
    b: $tType ).

thf(g_type,type,
    g: a > b ).

thf(f_type,type,
    f: a > b ).

thf(cQ_type,type,
    cQ: a > b > b > $o ).

thf(cP_type,type,
    cP: a > a > $o ).

thf(sk1_type,type,
    sk1: a ).

thf(sk2_type,type,
    sk2: a ).

thf(1,conjecture,
    ( ! [A: a] :
        ( ( cP @ A @ A )
       => ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) )
   => ( ! [A: a,B: a] :
          ( ( cP @ A @ B )
         => ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) )
     => ( ( ! [A: a,B: a] :
              ( ( cP @ A @ B )
             => ( cP @ B @ A ) )
          & ! [A: a,B: a,C: a] :
              ( ( ( cP @ A @ B )
                & ( cP @ B @ C ) )
             => ( cP @ A @ C ) ) )
       => ( ( ! [A: a] :
                ( ( cP @ A @ A )
               => ( ! [B: b,C: b] :
                      ( ( cQ @ A @ B @ C )
                     => ( cQ @ A @ C @ B ) )
                  & ! [B: b,C: b,D: b] :
                      ( ( ( cQ @ A @ B @ C )
                        & ( cQ @ A @ C @ D ) )
                     => ( cQ @ A @ B @ D ) ) ) )
            & ! [A: a,B: a] :
                ( ( cP @ A @ B )
               => ( ( cQ @ A )
                  = ( cQ @ B ) ) ) )
         => ! [A: a,B: a] :
              ( ( cP @ A @ B )
             => ( cQ @ A @ ( f @ A ) @ ( g @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM509_pme) ).

thf(2,negated_conjecture,
    ~ ( ! [A: a] :
          ( ( cP @ A @ A )
         => ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) )
     => ( ! [A: a,B: a] :
            ( ( cP @ A @ B )
           => ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) )
       => ( ( ! [A: a,B: a] :
                ( ( cP @ A @ B )
               => ( cP @ B @ A ) )
            & ! [A: a,B: a,C: a] :
                ( ( ( cP @ A @ B )
                  & ( cP @ B @ C ) )
               => ( cP @ A @ C ) ) )
         => ( ( ! [A: a] :
                  ( ( cP @ A @ A )
                 => ( ! [B: b,C: b] :
                        ( ( cQ @ A @ B @ C )
                       => ( cQ @ A @ C @ B ) )
                    & ! [B: b,C: b,D: b] :
                        ( ( ( cQ @ A @ B @ C )
                          & ( cQ @ A @ C @ D ) )
                       => ( cQ @ A @ B @ D ) ) ) )
              & ! [A: a,B: a] :
                  ( ( cP @ A @ B )
                 => ( ( cQ @ A )
                    = ( cQ @ B ) ) ) )
           => ! [A: a,B: a] :
                ( ( cP @ A @ B )
               => ( cQ @ A @ ( f @ A ) @ ( g @ B ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: a] :
          ( ( cP @ A @ A )
         => ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) )
     => ( ! [A: a,B: a] :
            ( ( cP @ A @ B )
           => ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) )
       => ( ( ! [A: a,B: a] :
                ( ( cP @ A @ B )
               => ( cP @ B @ A ) )
            & ! [A: a,B: a,C: a] :
                ( ( ( cP @ A @ B )
                  & ( cP @ B @ C ) )
               => ( cP @ A @ C ) ) )
         => ( ( ! [A: a] :
                  ( ( cP @ A @ A )
                 => ( ! [B: b,C: b] :
                        ( ( cQ @ A @ B @ C )
                       => ( cQ @ A @ C @ B ) )
                    & ! [B: b,C: b,D: b] :
                        ( ( ( cQ @ A @ B @ C )
                          & ( cQ @ A @ C @ D ) )
                       => ( cQ @ A @ B @ D ) ) ) )
              & ! [A: a,B: a] :
                  ( ( cP @ A @ B )
                 => ( ( cQ @ A )
                    = ( cQ @ B ) ) ) )
           => ! [A: a,B: a] :
                ( ( cP @ A @ B )
               => ( cQ @ A @ ( f @ A ) @ ( g @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    cP @ sk1 @ sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ( ( cQ @ A )
        = ( cQ @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [B: a,A: a] :
      ( ( ( cQ @ A )
        = ( cQ @ B ) )
      | ~ ( cP @ A @ B ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(15,plain,
    ! [B: a,A: a] :
      ( ( ( cQ @ A )
        = ( cQ @ B ) )
      | ~ ( cP @ A @ B ) ),
    inference(simp,[status(thm)],[14]) ).

thf(64,plain,
    ! [B: a,A: a] :
      ( ( ( cQ @ A )
        = ( cQ @ B ) )
      | ( ( cP @ sk1 @ sk2 )
       != ( cP @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,15]) ).

thf(65,plain,
    ( ( cQ @ sk2 )
    = ( cQ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(71,plain,
    ! [B: b,A: b] :
      ( ( cQ @ sk2 @ A @ B )
      = ( cQ @ sk1 @ A @ B ) ),
    inference(func_ext,[status(esa)],[65]) ).

thf(11,plain,
    ! [A: a] :
      ( ~ ( cP @ A @ A )
      | ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(115,plain,
    ! [C: a,B: b,A: b] :
      ( ~ ( cP @ C @ C )
      | ( cQ @ sk1 @ A @ B )
      | ( ( cQ @ sk2 @ A @ B )
       != ( cQ @ C @ ( f @ C ) @ ( g @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[71,11]) ).

thf(116,plain,
    ( ~ ( cP @ sk2 @ sk2 )
    | ( cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( f @ sk2 )),bind(B,$thf( g @ sk2 )),bind(C,$thf( sk2 ))]]) ).

thf(8,plain,
    ! [B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ( cP @ B @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(18,plain,
    ! [B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ( cP @ B @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(22,plain,
    ! [B: a,A: a] :
      ( ( cP @ B @ A )
      | ( ( cP @ sk1 @ sk2 )
       != ( cP @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,18]) ).

thf(23,plain,
    cP @ sk2 @ sk1,
    inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(9,plain,
    ! [C: a,B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ~ ( cP @ B @ C )
      | ( cP @ A @ C ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(16,plain,
    ! [C: a,B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ~ ( cP @ B @ C )
      | ( cP @ A @ C ) ),
    inference(simp,[status(thm)],[9]) ).

thf(228,plain,
    ! [C: a,B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ( cP @ A @ C )
      | ( ( cP @ sk1 @ sk2 )
       != ( cP @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[5,16]) ).

thf(229,plain,
    ! [A: a] :
      ( ~ ( cP @ A @ sk1 )
      | ( cP @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).

thf(419,plain,
    ! [A: a] :
      ( ( cP @ A @ sk2 )
      | ( ( cP @ sk2 @ sk1 )
       != ( cP @ A @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[23,229]) ).

thf(420,plain,
    cP @ sk2 @ sk2,
    inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( sk2 ))]]) ).

thf(447,plain,
    ( ~ $true
    | ( cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ) ) ),
    inference(rewrite,[status(thm)],[116,420]) ).

thf(448,plain,
    cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ),
    inference(simp,[status(thm)],[447]) ).

thf(4,plain,
    ! [D: b,C: b,B: b,A: a] :
      ( ~ ( cP @ A @ A )
      | ~ ( cQ @ A @ B @ C )
      | ~ ( cQ @ A @ C @ D )
      | ( cQ @ A @ B @ D ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(19,plain,
    ! [D: b,C: b,B: b,A: a] :
      ( ~ ( cP @ A @ A )
      | ~ ( cQ @ A @ B @ C )
      | ~ ( cQ @ A @ C @ D )
      | ( cQ @ A @ B @ D ) ),
    inference(simp,[status(thm)],[4]) ).

thf(7,plain,
    ~ ( cQ @ sk1 @ ( f @ sk1 ) @ ( g @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(27,plain,
    ! [D: b,C: b,B: b,A: a] :
      ( ~ ( cP @ A @ A )
      | ~ ( cQ @ A @ B @ C )
      | ~ ( cQ @ A @ C @ D )
      | ( ( cQ @ A @ B @ D )
       != ( cQ @ sk1 @ ( f @ sk1 ) @ ( g @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,7]) ).

thf(28,plain,
    ! [A: b] :
      ( ~ ( cP @ sk1 @ sk1 )
      | ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
      | ~ ( cQ @ sk1 @ A @ ( g @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk1 )),bind(B,$thf( f @ sk1 )),bind(C,$thf( C )),bind(D,$thf( g @ sk2 ))]]) ).

thf(44,plain,
    ! [A: b] :
      ( ~ ( cP @ sk1 @ sk1 )
      | ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
      | ~ ( cQ @ sk1 @ A @ ( g @ sk2 ) ) ),
    inference(simp,[status(thm)],[28]) ).

thf(52,plain,
    ! [A: b] :
      ( ~ ( cP @ sk1 @ sk1 )
      | ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
      | ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
       != ( cQ @ sk1 @ ( f @ sk1 ) @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[44]) ).

thf(53,plain,
    ! [A: b] :
      ( ~ ( cP @ sk1 @ sk1 )
      | ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
      | ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
       != ( cQ @ sk1 @ ( f @ sk1 ) @ A ) ) ),
    inference(simp,[status(thm)],[52]) ).

thf(250,plain,
    ! [C: a,B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ( cP @ A @ C )
      | ( ( cP @ sk2 @ sk1 )
       != ( cP @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[23,16]) ).

thf(251,plain,
    ! [A: a] :
      ( ~ ( cP @ A @ sk2 )
      | ( cP @ A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).

thf(860,plain,
    ! [A: a] :
      ( ( cP @ A @ sk1 )
      | ( ( cP @ sk1 @ sk2 )
       != ( cP @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[5,251]) ).

thf(861,plain,
    cP @ sk1 @ sk1,
    inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( sk1 ))]]) ).

thf(1043,plain,
    ! [A: b] :
      ( ~ $true
      | ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
      | ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
       != ( cQ @ sk1 @ ( f @ sk1 ) @ A ) ) ),
    inference(rewrite,[status(thm)],[53,861]) ).

thf(1044,plain,
    ! [A: b] :
      ( ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
      | ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
       != ( cQ @ sk1 @ ( f @ sk1 ) @ A ) ) ),
    inference(simp,[status(thm)],[1043]) ).

thf(1073,plain,
    ! [A: b] :
      ( ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
      | ( ( cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ) )
       != ( cQ @ sk1 @ A @ ( g @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[448,1044]) ).

thf(1074,plain,
    ~ ( cQ @ sk1 @ ( f @ sk1 ) @ ( f @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[1073:[bind(A,$thf( f @ sk2 ))]]) ).

thf(10,plain,
    ! [B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [B: a,A: a] :
      ( ~ ( cP @ A @ B )
      | ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(151,plain,
    ! [B: a,A: a] :
      ( ( cQ @ A @ ( f @ A ) @ ( f @ B ) )
      | ( ( cP @ sk1 @ sk2 )
       != ( cP @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,13]) ).

thf(152,plain,
    cQ @ sk1 @ ( f @ sk1 ) @ ( f @ sk2 ),
    inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(1182,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[1074,152]) ).

thf(1183,plain,
    $false,
    inference(simp,[status(thm)],[1182]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEV045^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 18:50:23 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.89/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.97  % [INFO] 	 Parsing done (109ms). 
% 1.23/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.56/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.56/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.97/1.28  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.97/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.97/1.29  % [INFO] 	 Type checking passed. 
% 1.97/1.29  % [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 ... 
% 9.10/2.72  % [INFO] 	 Killing All external provers ... 
% 9.10/2.73  % Time passed: 2199ms (effective reasoning time: 1740ms)
% 9.10/2.74  % 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)>
% 9.10/2.74  % Axioms used in derivation (0): 
% 9.10/2.74  % No. of inferences in proof: 47
% 9.10/2.74  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2199 ms resp. 1740 ms w/o parsing
% 9.13/2.80  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.13/2.80  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------