TSTP Solution File: AGT034^1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : AGT034^1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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  7 10:24:49 EDT 2024

% Result   : Theorem 64.59s 10.23s
% Output   : Refutation 64.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   67 (  19 unt;  22 typ;   7 def)
%            Number of atoms       :  147 (  14 equ;   0 cnn)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  416 (  52   ~;  40   |;   0   &; 322   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   68 (  68   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;  10 con; 0-4 aty)
%            Number of variables   :   74 (  15   ^  58   !;   1   ?;  74   :)

% 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(mforall_ind_type,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

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

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(mdia_type,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).

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

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

thf(a1_type,type,
    a1: $i > $i > $o ).

thf(a2_type,type,
    a2: $i > $i > $o ).

thf(a3_type,type,
    a3: $i > $i > $o ).

thf(jan_type,type,
    jan: mu ).

thf(piotr_type,type,
    piotr: mu ).

thf(cola_type,type,
    cola: mu ).

thf(pepsi_type,type,
    pepsi: mu ).

thf(likes_type,type,
    likes: mu > mu > $i > $o ).

thf(very_much_likes_type,type,
    very_much_likes: mu > mu > $i > $o ).

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

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

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

thf(sk8_type,type,
    sk8: $i > mu > mu > $i > $i ).

thf(sk9_type,type,
    sk9: $i > mu > mu > $i > $i ).

thf(24,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [A: mu] :
          ( mforall_ind
          @ ^ [B: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ A @ B ) ) @ ( very_much_likes @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_user_communication_1) ).

thf(86,plain,
    ! [A: $i,B: mu,C: mu] :
      ( ~ ! [D: $i] :
            ( ~ ( a3 @ A @ D )
            | ( very_much_likes @ B @ C @ D ) )
      | ( very_much_likes @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(87,plain,
    ! [C: mu,B: mu,A: $i] :
      ( ( a3 @ A @ ( sk5 @ C @ B @ A ) )
      | ( very_much_likes @ B @ C @ A ) ),
    inference(cnf,[status(esa)],[86]) ).

thf(1,conjecture,
    mvalid @ ( very_much_likes @ jan @ cola ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( very_much_likes @ jan @ cola ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(42,plain,
    ~ ! [A: $i] : ( very_much_likes @ jan @ cola @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(43,plain,
    ~ ( very_much_likes @ jan @ cola @ sk1 ),
    inference(cnf,[status(esa)],[42]) ).

thf(734,plain,
    ! [C: mu,B: mu,A: $i] :
      ( ( a3 @ A @ ( sk5 @ C @ B @ A ) )
      | ( ( very_much_likes @ B @ C @ A )
       != ( very_much_likes @ jan @ cola @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[87,43]) ).

thf(735,plain,
    a3 @ sk1 @ ( sk5 @ cola @ jan @ sk1 ),
    inference(pattern_uni,[status(thm)],[734:[bind(A,$thf( sk1 )),bind(B,$thf( jan )),bind(C,$thf( cola ))]]) ).

thf(8,axiom,
    msymmetric @ a3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axioms_B_a3) ).

thf(54,plain,
    ! [A: $i,B: $i] :
      ( ( a3 @ A @ B )
     => ( a3 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a3 @ A @ B )
      | ( a3 @ B @ A ) ),
    inference(cnf,[status(esa)],[54]) ).

thf(1872,plain,
    ! [B: $i,A: $i] :
      ( ( a3 @ B @ A )
      | ( ( a3 @ sk1 @ ( sk5 @ cola @ jan @ sk1 ) )
       != ( a3 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[735,55]) ).

thf(1873,plain,
    a3 @ ( sk5 @ cola @ jan @ sk1 ) @ sk1,
    inference(pattern_uni,[status(thm)],[1872:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 @ cola @ jan @ sk1 ))]]) ).

thf(38,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [A: mu] :
          ( mforall_ind
          @ ^ [B: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ A @ B ) @ ( mand @ ( mbox @ a1 @ ( likes @ A @ B ) ) @ ( mbox @ a2 @ ( likes @ A @ B ) ) ) ) @ ( very_much_likes @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a3_4) ).

thf(119,plain,
    ! [A: $i,B: mu,C: mu,D: $i] :
      ( ~ ( a3 @ A @ D )
      | ~ ( likes @ B @ C @ D )
      | ~ ! [E: $i] :
            ( ~ ( a1 @ D @ E )
            | ( likes @ B @ C @ E ) )
      | ~ ! [E: $i] :
            ( ~ ( a2 @ D @ E )
            | ( likes @ B @ C @ E ) )
      | ( very_much_likes @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(120,plain,
    ! [D: $i,C: mu,B: mu,A: $i] :
      ( ~ ( a3 @ A @ D )
      | ~ ( likes @ B @ C @ D )
      | ~ ( likes @ B @ C @ ( sk8 @ D @ C @ B @ A ) )
      | ~ ( likes @ B @ C @ ( sk9 @ D @ C @ B @ A ) )
      | ( very_much_likes @ B @ C @ D ) ),
    inference(cnf,[status(esa)],[119]) ).

thf(140,plain,
    ! [D: $i,C: mu,B: mu,A: $i] :
      ( ~ ( a3 @ A @ D )
      | ~ ( likes @ B @ C @ D )
      | ~ ( likes @ B @ C @ ( sk8 @ D @ C @ B @ A ) )
      | ~ ( likes @ B @ C @ ( sk9 @ D @ C @ B @ A ) )
      | ( ( very_much_likes @ B @ C @ D )
       != ( very_much_likes @ jan @ cola @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[120,43]) ).

thf(141,plain,
    ! [A: $i] :
      ( ~ ( a3 @ A @ sk1 )
      | ~ ( likes @ jan @ cola @ sk1 )
      | ~ ( likes @ jan @ cola @ ( sk8 @ sk1 @ cola @ jan @ A ) )
      | ~ ( likes @ jan @ cola @ ( sk9 @ sk1 @ cola @ jan @ A ) ) ),
    inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( A )),bind(B,$thf( jan )),bind(C,$thf( cola )),bind(D,$thf( sk1 ))]]) ).

thf(169,plain,
    ! [A: $i] :
      ( ~ ( a3 @ A @ sk1 )
      | ~ ( likes @ jan @ cola @ sk1 )
      | ~ ( likes @ jan @ cola @ ( sk8 @ sk1 @ cola @ jan @ A ) )
      | ( ( likes @ jan @ cola @ ( sk9 @ sk1 @ cola @ jan @ A ) )
       != ( likes @ jan @ cola @ ( sk8 @ sk1 @ cola @ jan @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[141]) ).

thf(172,plain,
    ! [A: $i] :
      ( ~ ( a3 @ A @ sk1 )
      | ~ ( likes @ jan @ cola @ sk1 )
      | ~ ( likes @ jan @ cola @ ( sk8 @ sk1 @ cola @ jan @ A ) )
      | ( ( likes @ jan @ cola @ ( sk9 @ sk1 @ cola @ jan @ A ) )
       != ( likes @ jan @ cola @ ( sk8 @ sk1 @ cola @ jan @ A ) ) ) ),
    inference(simp,[status(thm)],[169]) ).

thf(26,axiom,
    mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a3_2) ).

thf(91,plain,
    ! [A: $i] :
      ~ ! [B: $i] :
          ( ~ ( a3 @ A @ B )
          | ~ ( likes @ piotr @ pepsi @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(92,plain,
    ~ ? [A: $i] :
      ! [B: $i] :
        ( ~ ( a3 @ A @ B )
        | ~ ( likes @ piotr @ pepsi @ B ) ),
    inference(miniscope,[status(thm)],[91]) ).

thf(94,plain,
    ! [A: $i] : ( a3 @ A @ ( sk6 @ A ) ),
    inference(cnf,[status(esa)],[92]) ).

thf(1874,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a3 @ C @ B )
      | ( ( a3 @ A @ ( sk6 @ A ) )
       != ( a3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[94,55]) ).

thf(1875,plain,
    ! [A: $i] : ( a3 @ ( sk6 @ A ) @ A ),
    inference(pattern_uni,[status(thm)],[1874:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk6 @ D ))]]) ).

thf(1877,plain,
    ! [A: $i] : ( a3 @ ( sk6 @ A ) @ A ),
    inference(simp,[status(thm)],[1875]) ).

thf(39,axiom,
    mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a3_1) ).

thf(124,plain,
    ! [A: $i,B: $i] :
      ( ~ ( a3 @ A @ B )
      | ( likes @ jan @ cola @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(125,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a3 @ A @ B )
      | ( likes @ jan @ cola @ B ) ),
    inference(cnf,[status(esa)],[124]) ).

thf(1975,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( likes @ jan @ cola @ C )
      | ( ( a3 @ ( sk6 @ A ) @ A )
       != ( a3 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1877,125]) ).

thf(1976,plain,
    ! [A: $i] : ( likes @ jan @ cola @ A ),
    inference(pattern_uni,[status(thm)],[1975:[bind(A,$thf( D )),bind(B,$thf( sk6 @ D )),bind(C,$thf( D ))]]) ).

thf(1983,plain,
    ! [A: $i] : ( likes @ jan @ cola @ A ),
    inference(simp,[status(thm)],[1976]) ).

thf(12357,plain,
    ! [A: $i] :
      ( ~ ( a3 @ A @ sk1 )
      | ~ $true
      | ~ $true
      | ~ $true ),
    inference(rewrite,[status(thm)],[172,1983]) ).

thf(12358,plain,
    ! [A: $i] :
      ~ ( a3 @ A @ sk1 ),
    inference(simp,[status(thm)],[12357]) ).

thf(12391,plain,
    $false,
    inference(rewrite,[status(thm)],[1873,12358]) ).

thf(12392,plain,
    $false,
    inference(simp,[status(thm)],[12391]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : AGT034^1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.04/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n017.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 : Mon May  6 22:28:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.96/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.43/1.06  % [INFO] 	 Parsing done (179ms). 
% 1.43/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.95/1.30  % [INFO] 	 nitpick registered as external prover. 
% 1.95/1.30  % [INFO] 	 Scanning for conjecture ... 
% 2.22/1.43  % [INFO] 	 Found a conjecture and 39 axioms. Running axiom selection ... 
% 2.49/1.48  % [INFO] 	 Axiom selection finished. Selected 39 axioms (removed 0 axioms). 
% 2.66/1.49  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.66/1.50  % [INFO] 	 Type checking passed. 
% 2.66/1.50  % [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 ... 
% 64.59/10.22  % [INFO] 	 Killing All external provers ... 
% 64.59/10.22  % Time passed: 9696ms (effective reasoning time: 9153ms)
% 64.59/10.22  % 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)>
% 64.59/10.23  % Axioms used in derivation (5): axiom_a3_4, axiom_a3_1, axiom_a3_2, axiom_user_communication_1, axioms_B_a3
% 64.59/10.23  % No. of inferences in proof: 38
% 64.59/10.23  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9696 ms resp. 9153 ms w/o parsing
% 64.59/10.27  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.59/10.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------