TSTP Solution File: QUA006^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : QUA006^1 : TPTP v8.2.0. Released v4.1.0.
% 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 21 02:30:26 EDT 2024

% Result   : Theorem 31.45s 7.87s
% Output   : Refutation 31.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   42 (  29 unt;   8 typ;   3 def)
%            Number of atoms       :   70 (  53 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :  125 (  12   ~;   5   |;  12   &;  96   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   65 (  27   ^  26   !;  12   ?;  65   :)

% Comments : 
%------------------------------------------------------------------------------
thf(emptyset_type,type,
    emptyset: $i > $o ).

thf(emptyset_def,definition,
    ( emptyset
    = ( ^ [A: $i] : $false ) ) ).

thf(singleton_type,type,
    singleton: $i > $i > $o ).

thf(singleton_def,definition,
    ( singleton
    = ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).

thf(zero_type,type,
    zero: $i ).

thf(sup_type,type,
    sup: ( $i > $o ) > $i ).

thf(multiplication_type,type,
    multiplication: $i > $i > $i ).

thf(crossmult_type,type,
    crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(crossmult_def,definition,
    ( crossmult
    = ( ^ [A: $i > $o,B: $i > $o,C: $i] :
        ? [D: $i,E: $i] :
          ( ( A @ D )
          & ( B @ E )
          & ( C
            = ( multiplication @ D @ E ) ) ) ) ) ).

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

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

thf(4,axiom,
    ! [A: $i] :
      ( ( sup @ ( singleton @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sup_singleset) ).

thf(15,plain,
    ! [A: $i] :
      ( ( sup
        @ ^ [B: $i] : ( B = A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(16,plain,
    ! [A: $i] :
      ( ( sup
        @ ^ [B: $i] : ( B = A ) )
      = A ),
    inference(cnf,[status(esa)],[15]) ).

thf(17,plain,
    ! [A: $i] :
      ( ( sup
        @ ^ [B: $i] : ( B = A ) )
      = A ),
    inference(lifteq,[status(thm)],[16]) ).

thf(3,axiom,
    ( ( sup @ emptyset )
    = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sup_es) ).

thf(13,plain,
    ( ( sup
      @ ^ [A: $i] : $false )
    = zero ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    ( ( sup
      @ ^ [A: $i] : $false )
    = zero ),
    inference(lifteq,[status(thm)],[13]) ).

thf(36,plain,
    ! [A: $i] :
      ( ( A = zero )
      | ( ( sup
          @ ^ [B: $i] : ( B = A ) )
       != ( sup
          @ ^ [B: $i] : $false ) ) ),
    inference(paramod_ordered,[status(thm)],[17,14]) ).

thf(39,plain,
    ! [A: $i] :
      ( ( A = zero )
      | ( ( ^ [B: $i] : ( B = A ) )
       != ( ^ [B: $i] : $false ) ) ),
    inference(simp,[status(thm)],[36]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( multiplication @ zero @ A )
      = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_anni) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( multiplication @ zero @ A )
        = zero ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: $i] :
        ( ( multiplication @ zero @ A )
        = zero ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    ( ( multiplication @ zero @ sk1 )
   != zero ),
    inference(cnf,[status(esa)],[10]) ).

thf(12,plain,
    ( ( multiplication @ zero @ sk1 )
   != zero ),
    inference(lifteq,[status(thm)],[11]) ).

thf(226,plain,
    ! [A: $i] :
      ( ( ( ^ [B: $i] : ( B = A ) )
       != ( ^ [B: $i] : $false ) )
      | ( A
       != ( multiplication @ zero @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[39,12]) ).

thf(227,plain,
    ( ( ^ [A: $i] :
          ( A
          = ( multiplication @ zero @ sk1 ) ) )
   != ( ^ [A: $i] : $false ) ),
    inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( multiplication @ zero @ sk1 ))]]) ).

thf(275,plain,
    ( sk3
    = ( multiplication @ zero @ sk1 ) ),
    inference(func_ext,[status(esa)],[227]) ).

thf(289,plain,
    ( ( multiplication @ zero @ sk1 )
    = sk3 ),
    inference(lifteq,[status(thm)],[275]) ).

thf(7,axiom,
    ! [A: $i > $o,B: $i > $o] :
      ( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
      = ( sup @ ( crossmult @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_def) ).

thf(24,plain,
    ! [A: $i > $o,B: $i > $o] :
      ( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
      = ( sup
        @ ^ [C: $i] :
          ? [D: $i,E: $i] :
            ( ( A @ D )
            & ( B @ E )
            & ( C
              = ( multiplication @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(25,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
      = ( sup
        @ ^ [C: $i] :
          ? [D: $i,E: $i] :
            ( ( A @ D )
            & ( B @ E )
            & ( C
              = ( multiplication @ D @ E ) ) ) ) ),
    inference(cnf,[status(esa)],[24]) ).

thf(26,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
      = ( sup
        @ ^ [C: $i] :
          ? [D: $i,E: $i] :
            ( ( A @ D )
            & ( B @ E )
            & ( C
              = ( multiplication @ D @ E ) ) ) ) ),
    inference(lifteq,[status(thm)],[25]) ).

thf(688,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ( ( multiplication @ zero @ ( sup @ B ) )
        = ( sup
          @ ^ [C: $i] :
            ? [D: $i,E: $i] :
              ( ( A @ D )
              & ( B @ E )
              & ( C
                = ( multiplication @ D @ E ) ) ) ) )
      | ( ( sup
          @ ^ [C: $i] : $false )
       != ( sup @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[14,26]) ).

thf(689,plain,
    ! [A: $i > $o] :
      ( ( multiplication @ zero @ ( sup @ A ) )
      = ( sup
        @ ^ [B: $i] :
          ? [C: $i,D: $i] :
            ( $false
            & ( A @ D )
            & ( B
              = ( multiplication @ C @ D ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[688:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).

thf(824,plain,
    ! [A: $i > $o] :
      ( ( multiplication @ zero @ ( sup @ A ) )
      = ( sup
        @ ^ [B: $i] : $false ) ),
    inference(simp,[status(thm)],[689]) ).

thf(840,plain,
    ! [A: $i > $o] :
      ( ( multiplication @ zero @ ( sup @ A ) )
      = zero ),
    inference(rewrite,[status(thm)],[824,14]) ).

thf(869,plain,
    ! [B: $i > $o,A: $i] :
      ( ( ( multiplication @ zero @ A )
        = zero )
      | ( ( sup
          @ ^ [C: $i] : ( C = A ) )
       != ( sup @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[17,840]) ).

thf(870,plain,
    ! [A: $i] :
      ( ( multiplication @ zero @ A )
      = zero ),
    inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : ( C = A ) ))]]) ).

thf(947,plain,
    sk3 = zero,
    inference(rewrite,[status(thm)],[289,870]) ).

thf(294,plain,
    sk3 != zero,
    inference(rewrite,[status(thm)],[12,289]) ).

thf(975,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[947,294]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : QUA006^1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.38  % Computer : n017.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit : 300
% 0.16/0.38  % WCLimit  : 300
% 0.16/0.38  % DateTime : Mon May 20 13:37:39 EDT 2024
% 0.16/0.38  % CPUTime  : 
% 0.95/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.29/1.00  % [INFO] 	 Parsing done (122ms). 
% 1.29/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.81/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.81/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.04/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 2.04/1.36  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 2.13/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.13/1.37  % [INFO] 	 Type checking passed. 
% 2.13/1.37  % [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 ... 
% 31.45/7.86  % [INFO] 	 Killing All external provers ... 
% 31.45/7.87  % Time passed: 7333ms (effective reasoning time: 6849ms)
% 31.45/7.87  % 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)>
% 31.45/7.87  % Axioms used in derivation (3): sup_singleset, sup_es, multiplication_def
% 31.45/7.87  % No. of inferences in proof: 31
% 31.45/7.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7333 ms resp. 6849 ms w/o parsing
% 31.45/7.89  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.45/7.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------