TSTP Solution File: SYO443^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO443^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 09:00:16 EDT 2024

% Result   : Theorem 20.70s 4.53s
% Output   : Refutation 20.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   80 (  14 unt;  18 typ;   7 def)
%            Number of atoms       :  236 (  18 equ;   0 cnn)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  491 ( 106   ~; 111   |;   2   &; 268   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   38 (  38   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  20 usr;  12 con; 0-3 aty)
%            Number of variables   :   78 (  11   ^  67   !;   0   ?;  78   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: $i > $o,B: $i] :
          ~ ( A @ B ) ) ) ).

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mor_def,definition,
    ( mor
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
          ( ( A @ C )
          | ( B @ C ) ) ) ) ).

thf(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

thf(msymmetric_def,definition,
    ( msymmetric
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i] :
          ( ( A @ B @ C )
         => ( A @ C @ B ) ) ) ) ).

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(mtransitive_def,definition,
    ( mtransitive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) ) ) ) ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

thf(rel_s5_type,type,
    rel_s5: $i > $i > $o ).

thf(mbox_s5_type,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

thf(mbox_s5_def,definition,
    ( mbox_s5
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_s5 @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(p_type,type,
    p: $i > $o ).

thf(q_type,type,
    q: $i > $o ).

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

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

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

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

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i ).

thf(sk7_type,type,
    sk7: $i ).

thf(1,conjecture,
    mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: $i] :
        ~ ( ~ ( ~ ! [B: $i] :
                    ( ~ ( rel_s5 @ A @ B )
                    | ~ ( p @ B )
                    | ! [C: $i] :
                        ( ~ ( rel_s5 @ B @ C )
                        | ( q @ C ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ( q @ B ) ) )
          | ~ ( ~ ( ! [B: $i] :
                      ( ~ ( rel_s5 @ A @ B )
                      | ~ ( p @ B ) )
                  | ! [B: $i] :
                      ( ~ ( rel_s5 @ A @ B )
                      | ( q @ B ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B )
                  | ! [C: $i] :
                      ( ~ ( rel_s5 @ B @ C )
                      | ( q @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ~ ~ ( ~ ! [A: $i] :
              ( ~ ! [B: $i] :
                    ( ~ ( rel_s5 @ A @ B )
                    | ~ ( p @ B )
                    | ! [C: $i] :
                        ( ~ ( rel_s5 @ B @ C )
                        | ( q @ C ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ( q @ B ) ) )
        | ~ ! [A: $i] :
              ( ~ ( ! [B: $i] :
                      ( ~ ( rel_s5 @ A @ B )
                      | ~ ( p @ B ) )
                  | ! [B: $i] :
                      ( ~ ( rel_s5 @ A @ B )
                      | ( q @ B ) ) )
              | ! [B: $i] :
                  ( ~ ( rel_s5 @ A @ B )
                  | ~ ( p @ B )
                  | ! [C: $i] :
                      ( ~ ( rel_s5 @ B @ C )
                      | ( q @ C ) ) ) ) ),
    inference(miniscope,[status(thm)],[6]) ).

thf(12,plain,
    ( ( rel_s5 @ sk2 @ sk3 )
    | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(5,axiom,
    msymmetric @ rel_s5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).

thf(23,plain,
    ! [A: $i,B: $i] :
      ( ( rel_s5 @ A @ B )
     => ( rel_s5 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(24,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ( rel_s5 @ B @ A ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(76,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( rel_s5 @ B @ A )
      | ( ( rel_s5 @ sk2 @ sk3 )
       != ( rel_s5 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,24]) ).

thf(77,plain,
    ( sk1
    | ( rel_s5 @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(9,plain,
    ( ( rel_s5 @ sk2 @ sk4 )
    | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(4,axiom,
    mtransitive @ rel_s5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).

thf(21,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( rel_s5 @ A @ B )
        & ( rel_s5 @ B @ C ) )
     => ( rel_s5 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( rel_s5 @ A @ B )
      | ~ ( rel_s5 @ B @ C )
      | ( rel_s5 @ A @ C ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( sk1
      | ~ ( rel_s5 @ A @ B )
      | ( rel_s5 @ A @ C )
      | ( ( rel_s5 @ sk2 @ sk4 )
       != ( rel_s5 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[9,22]) ).

thf(251,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( rel_s5 @ A @ sk2 )
      | ( rel_s5 @ A @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(367,plain,
    ! [A: $i] :
      ( sk1
      | ( rel_s5 @ A @ sk4 )
      | ( ( rel_s5 @ sk3 @ sk2 )
       != ( rel_s5 @ A @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[77,251]) ).

thf(368,plain,
    ( sk1
    | ( rel_s5 @ sk3 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[367:[bind(A,$thf( sk3 ))]]) ).

thf(13,plain,
    ( ~ sk1
    | ( rel_s5 @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(14,plain,
    ( ~ sk1
    | ( rel_s5 @ sk6 @ sk7 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(242,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ A @ B )
      | ( rel_s5 @ A @ C )
      | ( ( rel_s5 @ sk6 @ sk7 )
       != ( rel_s5 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[14,22]) ).

thf(243,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ A @ sk6 )
      | ( rel_s5 @ A @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( sk6 )),bind(C,$thf( sk7 ))]]) ).

thf(1705,plain,
    ! [A: $i] :
      ( ~ sk1
      | ( rel_s5 @ A @ sk7 )
      | ( ( rel_s5 @ sk5 @ sk6 )
       != ( rel_s5 @ A @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[13,243]) ).

thf(1706,plain,
    ( ~ sk1
    | ( rel_s5 @ sk5 @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[1705:[bind(A,$thf( sk5 ))]]) ).

thf(10,plain,
    ( ~ sk1
    | ( p @ sk6 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ~ ( p @ A )
      | ~ ( rel_s5 @ sk5 @ B )
      | ( q @ B ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ~ ( p @ A )
      | ~ ( rel_s5 @ sk5 @ B )
      | ( q @ B ) ),
    inference(simp,[status(thm)],[17]) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ~ ( rel_s5 @ sk5 @ B )
      | ( q @ B )
      | ( ( p @ sk6 )
       != ( p @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,18]) ).

thf(26,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ sk6 )
      | ~ ( rel_s5 @ sk5 @ A )
      | ( q @ A ) ),
    inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( sk6 ))]]) ).

thf(34,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ sk6 )
      | ~ ( rel_s5 @ sk5 @ A )
      | ( q @ A ) ),
    inference(simp,[status(thm)],[26]) ).

thf(605,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ( q @ A )
      | ( ( rel_s5 @ sk5 @ sk6 )
       != ( rel_s5 @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[13,34]) ).

thf(606,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( rel_s5 @ sk5 @ A )
      | ( q @ A ) ),
    inference(pattern_uni,[status(thm)],[605:[]]) ).

thf(1763,plain,
    ! [A: $i] :
      ( ~ sk1
      | ( q @ A )
      | ( ( rel_s5 @ sk5 @ sk7 )
       != ( rel_s5 @ sk5 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1706,606]) ).

thf(1764,plain,
    ( ~ sk1
    | ( q @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[1763:[bind(A,$thf( sk7 ))]]) ).

thf(8,plain,
    ( ~ sk1
    | ~ ( q @ sk7 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(1812,plain,
    ( ~ sk1
    | ( ( q @ sk7 )
     != ( q @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[1764,8]) ).

thf(1813,plain,
    ~ sk1,
    inference(pattern_uni,[status(thm)],[1812:[]]) ).

thf(1836,plain,
    ( $false
    | ( rel_s5 @ sk3 @ sk4 ) ),
    inference(rewrite,[status(thm)],[368,1813]) ).

thf(1837,plain,
    rel_s5 @ sk3 @ sk4,
    inference(simp,[status(thm)],[1836]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rel_s5 @ sk2 @ A )
      | ~ ( p @ A )
      | ~ ( rel_s5 @ A @ B )
      | ( q @ B )
      | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(181,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ~ ( p @ A )
      | ~ ( rel_s5 @ A @ B )
      | ( q @ B )
      | ( ( rel_s5 @ sk2 @ sk3 )
       != ( rel_s5 @ sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12,15]) ).

thf(182,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( p @ sk3 )
      | ~ ( rel_s5 @ sk3 @ A )
      | ( q @ A ) ),
    inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( sk3 ))]]) ).

thf(197,plain,
    ! [A: $i] :
      ( sk1
      | ~ ( p @ sk3 )
      | ~ ( rel_s5 @ sk3 @ A )
      | ( q @ A ) ),
    inference(simp,[status(thm)],[182]) ).

thf(16,plain,
    ( ( p @ sk3 )
    | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(1832,plain,
    ( ( p @ sk3 )
    | $false ),
    inference(rewrite,[status(thm)],[16,1813]) ).

thf(1833,plain,
    p @ sk3,
    inference(simp,[status(thm)],[1832]) ).

thf(2575,plain,
    ! [A: $i] :
      ( $false
      | ~ $true
      | ~ ( rel_s5 @ sk3 @ A )
      | ( q @ A ) ),
    inference(rewrite,[status(thm)],[197,1813,1833]) ).

thf(2576,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk3 @ A )
      | ( q @ A ) ),
    inference(simp,[status(thm)],[2575]) ).

thf(2589,plain,
    ! [A: $i] :
      ( ( q @ A )
      | ( ( rel_s5 @ sk3 @ sk4 )
       != ( rel_s5 @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1837,2576]) ).

thf(2590,plain,
    q @ sk4,
    inference(pattern_uni,[status(thm)],[2589:[bind(A,$thf( sk4 ))]]) ).

thf(11,plain,
    ( ~ ( q @ sk4 )
    | sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(1834,plain,
    ( ~ ( q @ sk4 )
    | $false ),
    inference(rewrite,[status(thm)],[11,1813]) ).

thf(1835,plain,
    ~ ( q @ sk4 ),
    inference(simp,[status(thm)],[1834]) ).

thf(2614,plain,
    $false,
    inference(rewrite,[status(thm)],[2590,1835]) ).

thf(2615,plain,
    $false,
    inference(simp,[status(thm)],[2614]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SYO443^1 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n012.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Mon May 20 09:03:39 EDT 2024
% 0.17/0.38  % CPUTime  : 
% 0.92/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.25/1.08  % [INFO] 	 Parsing done (157ms). 
% 1.47/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.94/1.32  % [INFO] 	 nitpick registered as external prover. 
% 1.94/1.32  % [INFO] 	 Scanning for conjecture ... 
% 2.09/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.35/1.46  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.35/1.46  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.35/1.46  % [INFO] 	 Type checking passed. 
% 2.35/1.46  % [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 ... 
% 20.70/4.51  % [INFO] 	 Killing All external provers ... 
% 20.70/4.52  % Time passed: 3987ms (effective reasoning time: 3427ms)
% 20.70/4.52  % 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)>
% 20.70/4.52  % Axioms used in derivation (2): a3, a2
% 20.70/4.52  % No. of inferences in proof: 55
% 20.70/4.53  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3987 ms resp. 3427 ms w/o parsing
% 20.88/4.64  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.93/4.65  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------