TSTP Solution File: NUM755_8 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM755_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 10:45:32 EDT 2024

% Result   : Theorem 3.67s 1.96s
% Output   : Refutation 3.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   42 (  10 unt;   8 typ;   0 def)
%            Number of atoms       :   84 (   5 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  308 (  44   ~;  15   |;   0   &; 224   @)
%                                         (   0 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   58 (   0   ^  58   !;   0   ?;  58   :)

% Comments : 
%------------------------------------------------------------------------------
thf(frac_type,type,
    frac: $tType ).

thf(x_type,type,
    x: frac ).

thf(y_type,type,
    y: frac ).

thf(z_type,type,
    z: frac ).

thf(moref_type,type,
    moref: frac > frac > $o ).

thf(pf_type,type,
    pf: frac > frac > frac ).

thf(eq_type,type,
    eq: frac > frac > $o ).

thf(lessf_type,type,
    lessf: frac > frac > $o ).

thf(8,axiom,
    ! [A: frac,B: frac] :
      ( ~ ( eq @ A @ B )
     => ( ~ ( moref @ A @ B )
       => ( lessf @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41a) ).

thf(25,plain,
    ! [A: frac,B: frac] :
      ( ~ ( eq @ A @ B )
     => ( ~ ( moref @ A @ B )
       => ( lessf @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(26,plain,
    ! [B: frac,A: frac] :
      ( ( eq @ A @ B )
      | ( moref @ A @ B )
      | ( lessf @ A @ B ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(7,axiom,
    ! [A: frac,B: frac,C: frac] :
      ( ( lessf @ A @ B )
     => ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62c) ).

thf(22,plain,
    ! [A: frac,B: frac,C: frac] :
      ( ( lessf @ A @ B )
     => ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(23,plain,
    ! [A: frac,B: frac] :
      ( ( lessf @ A @ B )
     => ! [C: frac] : ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[22]) ).

thf(24,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ A @ B )
      | ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(3,axiom,
    moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(10,plain,
    moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [A: frac,B: frac] :
      ~ ( ( ( eq @ A @ B )
         => ~ ( moref @ A @ B ) )
       => ~ ~ ( ( ( moref @ A @ B )
               => ~ ( lessf @ A @ B ) )
             => ~ ( ( lessf @ A @ B )
                 => ~ ( eq @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41b) ).

thf(12,plain,
    ! [A: frac,B: frac] :
      ~ ( ( ( eq @ A @ B )
         => ~ ( moref @ A @ B ) )
       => ( ( ( moref @ A @ B )
           => ~ ( lessf @ A @ B ) )
         => ~ ( ( lessf @ A @ B )
             => ~ ( eq @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(13,plain,
    ~ ( ! [A: frac,B: frac] :
          ( ( eq @ A @ B )
         => ~ ( moref @ A @ B ) )
     => ( ! [A: frac,B: frac] :
            ( ( moref @ A @ B )
           => ~ ( lessf @ A @ B ) )
       => ~ ! [A: frac,B: frac] :
              ( ( lessf @ A @ B )
             => ~ ( eq @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[12]) ).

thf(15,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ B )
      | ~ ( lessf @ A @ B ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(18,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ B )
      | ~ ( lessf @ A @ B ) ),
    inference(simp,[status(thm)],[15]) ).

thf(33,plain,
    ! [B: frac,A: frac] :
      ( ~ ( lessf @ A @ B )
      | ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
       != ( moref @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10,18]) ).

thf(34,plain,
    ~ ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ y @ z ))]]) ).

thf(60,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ A @ B )
      | ( ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
       != ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,34]) ).

thf(61,plain,
    ~ ( lessf @ x @ y ),
    inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).

thf(68,plain,
    ! [B: frac,A: frac] :
      ( ( eq @ A @ B )
      | ( moref @ A @ B )
      | ( ( lessf @ A @ B )
       != ( lessf @ x @ y ) ) ),
    inference(paramod_ordered,[status(thm)],[26,61]) ).

thf(69,plain,
    ( ( eq @ x @ y )
    | ( moref @ x @ y ) ),
    inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).

thf(1,conjecture,
    moref @ x @ y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63a) ).

thf(2,negated_conjecture,
    ~ ( moref @ x @ y ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(9,plain,
    ~ ( moref @ x @ y ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ! [A: frac,B: frac,C: frac] :
      ( ( eq @ A @ B )
     => ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62b) ).

thf(19,plain,
    ! [A: frac,B: frac,C: frac] :
      ( ( eq @ A @ B )
     => ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(20,plain,
    ! [A: frac,B: frac] :
      ( ( eq @ A @ B )
     => ! [C: frac] : ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[19]) ).

thf(21,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
    inference(cnf,[status(esa)],[20]) ).

thf(16,plain,
    ! [B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ~ ( moref @ A @ B ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(29,plain,
    ! [B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
       != ( moref @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10,16]) ).

thf(30,plain,
    ~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ),
    inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ y @ z ))]]) ).

thf(41,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
       != ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
    inference(paramod_ordered,[status(thm)],[21,30]) ).

thf(42,plain,
    ~ ( eq @ x @ y ),
    inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).

thf(85,plain,
    ( $false
    | $false ),
    inference(rewrite,[status(thm)],[69,9,42]) ).

thf(86,plain,
    $false,
    inference(simp,[status(thm)],[85]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM755_8 : TPTP v8.1.2. Released v8.0.0.
% 0.07/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May  6 19:25:39 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.83/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.11/0.95  % [INFO] 	 Parsing done (135ms). 
% 1.11/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.57/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.57/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.65/1.28  % [INFO] 	 Found a conjecture and 6 axioms. Running axiom selection ... 
% 1.65/1.30  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 1.65/1.33  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.90/1.33  % [INFO] 	 Type checking passed. 
% 1.90/1.33  % [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 ... 
% 3.67/1.96  % [INFO] 	 Killing All external provers ... 
% 3.67/1.96  % Time passed: 1494ms (effective reasoning time: 991ms)
% 3.67/1.96  % 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)>
% 3.67/1.96  % Axioms used in derivation (5): satz41b, m, satz62b, satz62c, satz41a
% 3.67/1.96  % No. of inferences in proof: 34
% 3.67/1.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1494 ms resp. 991 ms w/o parsing
% 3.67/2.01  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/2.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------