TSTP Solution File: PUZ086^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : PUZ086^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May 21 02:27:26 EDT 2024

% Result   : Theorem 61.93s 10.23s
% Output   : Refutation 61.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   69 (  16 unt;  15 typ;   5 def)
%            Number of atoms       :  197 (  13 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  369 (  89   ~;  75   |;   0   &; 205   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   36 (  36   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;   9 con; 0-3 aty)
%            Number of variables   :   77 (   7   ^  70   !;   0   ?;  77   :)

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

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ~ ( A @ C @ D )
          | ( B @ D ) ) ) ) ).

thf(mreflexive_type,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(mreflexive_def,definition,
    ( mreflexive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i] : ( A @ B @ B ) ) ) ).

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

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

thf(peter_type,type,
    peter: $i > $i > $o ).

thf(john_type,type,
    john: $i > $i > $o ).

thf(time_type,type,
    time: $i > $o ).

thf(place_type,type,
    place: $i > $o ).

thf(appointment_type,type,
    appointment: $i > $o ).

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

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

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

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

thf(1,conjecture,
    mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(15,plain,
    ~ ! [A: $i] :
        ~ ( ~ ! [B: $i] :
                ( ~ ( peter @ A @ B )
                | ! [C: $i] :
                    ( ~ ( john @ B @ C )
                    | ( appointment @ C ) ) )
          | ~ ! [B: $i] :
                ( ~ ( john @ A @ B )
                | ! [C: $i] :
                    ( ~ ( peter @ B @ C )
                    | ( appointment @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(16,plain,
    ~ ~ ( ~ ! [A: $i,B: $i] :
              ( ~ ( peter @ A @ B )
              | ! [C: $i] :
                  ( ~ ( john @ B @ C )
                  | ( appointment @ C ) ) )
        | ~ ! [A: $i,B: $i] :
              ( ~ ( john @ A @ B )
              | ! [C: $i] :
                  ( ~ ( peter @ B @ C )
                  | ( appointment @ C ) ) ) ),
    inference(miniscope,[status(thm)],[15]) ).

thf(20,plain,
    ( ~ ( appointment @ sk4 )
    | sk1 ),
    inference(cnf,[status(esa)],[16]) ).

thf(4,axiom,
    mreflexive @ john,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_john) ).

thf(25,plain,
    ! [A: $i] : ( john @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(26,plain,
    ! [A: $i] : ( john @ A @ A ),
    inference(cnf,[status(esa)],[25]) ).

thf(21,plain,
    ( ~ sk1
    | ( peter @ sk6 @ sk7 ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(14,axiom,
    mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_d) ).

thf(49,plain,
    ! [A: $i,B: $i] :
      ( ~ ( peter @ A @ B )
      | ! [C: $i] :
          ( ~ ( john @ B @ C )
          | ~ ( place @ C )
          | ~ ( time @ C )
          | ( appointment @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(50,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( peter @ A @ B )
      | ~ ( john @ B @ C )
      | ~ ( place @ C )
      | ~ ( time @ C )
      | ( appointment @ C ) ),
    inference(cnf,[status(esa)],[49]) ).

thf(63,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ sk1
      | ~ ( john @ B @ C )
      | ~ ( place @ C )
      | ~ ( time @ C )
      | ( appointment @ C )
      | ( ( peter @ sk6 @ sk7 )
       != ( peter @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[21,50]) ).

thf(64,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( john @ sk7 @ A )
      | ~ ( place @ A )
      | ~ ( time @ A )
      | ( appointment @ A ) ),
    inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).

thf(65,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( john @ sk7 @ A )
      | ~ ( place @ A )
      | ~ ( time @ A )
      | ( appointment @ A ) ),
    inference(simp,[status(thm)],[64]) ).

thf(3,axiom,
    mreflexive @ peter,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_peter) ).

thf(23,plain,
    ! [A: $i] : ( peter @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

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

thf(11,axiom,
    mvalid @ ( mbox @ peter @ time ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_a) ).

thf(42,plain,
    ! [A: $i,B: $i] :
      ( ~ ( peter @ A @ B )
      | ( time @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ~ ( peter @ A @ B )
      | ( time @ B ) ),
    inference(cnf,[status(esa)],[42]) ).

thf(66,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( time @ C )
      | ( ( peter @ A @ A )
       != ( peter @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[24,43]) ).

thf(67,plain,
    ! [A: $i] : ( time @ A ),
    inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(84,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( john @ sk7 @ A )
      | ~ ( place @ A )
      | ~ $true
      | ( appointment @ A ) ),
    inference(rewrite,[status(thm)],[65,67]) ).

thf(85,plain,
    ! [A: $i] :
      ( ~ sk1
      | ~ ( john @ sk7 @ A )
      | ~ ( place @ A )
      | ( appointment @ A ) ),
    inference(simp,[status(thm)],[84]) ).

thf(88,plain,
    ! [B: $i,A: $i] :
      ( ~ sk1
      | ~ ( place @ B )
      | ( appointment @ B )
      | ( ( john @ A @ A )
       != ( john @ sk7 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[26,85]) ).

thf(89,plain,
    ( ~ sk1
    | ~ ( place @ sk7 )
    | ( appointment @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk7 )),bind(B,$thf( sk7 ))]]) ).

thf(22,plain,
    ( ~ sk1
    | ~ ( appointment @ sk7 ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(193,plain,
    ( ~ sk1
    | ~ ( place @ sk7 )
    | ( ( appointment @ sk7 )
     != ( appointment @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[89,22]) ).

thf(194,plain,
    ( ~ sk1
    | ~ ( place @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[193:[]]) ).

thf(12,axiom,
    mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_b) ).

thf(44,plain,
    ! [A: $i,B: $i] :
      ( ~ ( peter @ A @ B )
      | ! [C: $i] :
          ( ~ ( john @ B @ C )
          | ( place @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(45,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( peter @ A @ B )
      | ~ ( john @ B @ C )
      | ( place @ C ) ),
    inference(cnf,[status(esa)],[44]) ).

thf(4894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( peter @ B @ C )
      | ( place @ D )
      | ( ( john @ A @ A )
       != ( john @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[26,45]) ).

thf(4895,plain,
    ! [B: $i,A: $i] :
      ( ~ ( peter @ B @ A )
      | ( place @ A ) ),
    inference(pattern_uni,[status(thm)],[4894:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(5014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( place @ B )
      | ( ( peter @ A @ A )
       != ( peter @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[24,4895]) ).

thf(5015,plain,
    ! [A: $i] : ( place @ A ),
    inference(pattern_uni,[status(thm)],[5014:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(5073,plain,
    ( ~ sk1
    | ~ $true ),
    inference(rewrite,[status(thm)],[194,5015]) ).

thf(5074,plain,
    ~ sk1,
    inference(simp,[status(thm)],[5073]) ).

thf(5101,plain,
    ( ~ ( appointment @ sk4 )
    | $false ),
    inference(rewrite,[status(thm)],[20,5074]) ).

thf(5102,plain,
    ~ ( appointment @ sk4 ),
    inference(simp,[status(thm)],[5101]) ).

thf(53,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( peter @ B @ C )
      | ~ ( place @ D )
      | ~ ( time @ D )
      | ( appointment @ D )
      | ( ( john @ A @ A )
       != ( john @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[26,50]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ~ ( peter @ B @ A )
      | ~ ( place @ A )
      | ~ ( time @ A )
      | ( appointment @ A ) ),
    inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(5383,plain,
    ! [B: $i,A: $i] :
      ( ~ ( peter @ B @ A )
      | ~ $true
      | ~ $true
      | ( appointment @ A ) ),
    inference(rewrite,[status(thm)],[54,67,5015]) ).

thf(5384,plain,
    ! [B: $i,A: $i] :
      ( ~ ( peter @ B @ A )
      | ( appointment @ A ) ),
    inference(simp,[status(thm)],[5383]) ).

thf(5389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( appointment @ B )
      | ( ( peter @ A @ A )
       != ( peter @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[24,5384]) ).

thf(5390,plain,
    ! [A: $i] : ( appointment @ A ),
    inference(pattern_uni,[status(thm)],[5389:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).

thf(5424,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[5102,5390]) ).

thf(5425,plain,
    $false,
    inference(simp,[status(thm)],[5424]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : PUZ086^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat May 18 10:37:24 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.00/0.98  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.47/1.22  % [INFO] 	 Parsing done (240ms). 
% 1.47/1.23  % [INFO] 	 Running in sequential loop mode. 
% 2.17/1.60  % [INFO] 	 nitpick registered as external prover. 
% 2.17/1.60  % [INFO] 	 Scanning for conjecture ... 
% 2.63/1.78  % [INFO] 	 Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ... 
% 2.75/1.82  % [INFO] 	 Axiom selection finished. Selected 12 axioms (removed 0 axioms). 
% 2.75/1.82  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.75/1.83  % [INFO] 	 Type checking passed. 
% 2.75/1.83  % [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 ... 
% 61.19/10.20  % [INFO] 	 Killing All external provers ... 
% 61.93/10.20  % Time passed: 9705ms (effective reasoning time: 8961ms)
% 61.93/10.20  % 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)>
% 61.93/10.21  % Axioms used in derivation (5): ax_d, refl_peter, ax_b, ax_a, refl_john
% 61.93/10.23  % No. of inferences in proof: 49
% 61.93/10.23  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9705 ms resp. 8961 ms w/o parsing
% 61.95/10.37  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 61.95/10.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------