TSTP Solution File: NUM742^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM742^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 01:36:06 EDT 2024

% Result   : Theorem 13.29s 4.08s
% Output   : Refutation 13.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   45 (  13 unt;   6 typ;   0 def)
%            Number of atoms       :   96 (   6 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  247 (  28   ~;  26   |;   0   &; 174   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   60 (   0   ^  60   !;   0   ?;  60   :)

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

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

thf(4,axiom,
    lessf @ y @ z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).

thf(13,plain,
    lessf @ y @ z,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ( ~ ( lessf @ x @ y )
   => ( eq @ x @ y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).

thf(11,plain,
    ( ~ ( lessf @ x @ y )
   => ( eq @ x @ y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(12,plain,
    ( ( lessf @ x @ y )
    | ( eq @ x @ y ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(7,axiom,
    ! [A: frac,B: frac] :
      ( ( eq @ A @ B )
     => ( eq @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).

thf(18,plain,
    ! [A: frac,B: frac] :
      ( ( eq @ A @ B )
     => ( eq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(19,plain,
    ! [B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( eq @ B @ A ) ),
    inference(cnf,[status(esa)],[18]) ).

thf(111,plain,
    ! [B: frac,A: frac] :
      ( ( lessf @ x @ y )
      | ( eq @ B @ A )
      | ( ( eq @ x @ y )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,19]) ).

thf(112,plain,
    ( ( lessf @ x @ y )
    | ( eq @ y @ x ) ),
    inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).

thf(8,axiom,
    ! [A: frac,B: frac,C: frac] :
      ( ( lessf @ A @ B )
     => ( ( lessf @ B @ C )
       => ( lessf @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz50) ).

thf(20,plain,
    ! [A: frac,B: frac,C: frac] :
      ( ( lessf @ A @ B )
     => ( ( lessf @ B @ C )
       => ( lessf @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(21,plain,
    ! [A: frac,B: frac] :
      ( ( lessf @ A @ B )
     => ! [C: frac] :
          ( ( lessf @ B @ C )
         => ( lessf @ A @ C ) ) ),
    inference(miniscope,[status(thm)],[20]) ).

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

thf(159,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ A @ B )
      | ( lessf @ A @ C )
      | ( ( lessf @ y @ z )
       != ( lessf @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[13,22]) ).

thf(160,plain,
    ! [A: frac] :
      ( ~ ( lessf @ A @ y )
      | ( lessf @ A @ z ) ),
    inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).

thf(1,conjecture,
    lessf @ x @ z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51a) ).

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

thf(10,plain,
    ~ ( lessf @ x @ z ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(181,plain,
    ! [A: frac] :
      ( ~ ( lessf @ A @ y )
      | ( ( lessf @ A @ z )
       != ( lessf @ x @ z ) ) ),
    inference(paramod_ordered,[status(thm)],[160,10]) ).

thf(182,plain,
    ~ ( lessf @ x @ y ),
    inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( x ))]]) ).

thf(206,plain,
    ( $false
    | ( eq @ y @ x ) ),
    inference(rewrite,[status(thm)],[112,182]) ).

thf(207,plain,
    eq @ y @ x,
    inference(simp,[status(thm)],[206]) ).

thf(9,axiom,
    ! [A: frac] : ( eq @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).

thf(23,plain,
    ! [A: frac] : ( eq @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(24,plain,
    ! [A: frac] : ( eq @ A @ A ),
    inference(cnf,[status(esa)],[23]) ).

thf(6,axiom,
    ! [A: frac,B: frac,C: frac,D: frac] :
      ( ( lessf @ A @ B )
     => ( ( eq @ A @ C )
       => ( ( eq @ B @ D )
         => ( lessf @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz45) ).

thf(15,plain,
    ! [A: frac,B: frac,C: frac,D: frac] :
      ( ( lessf @ A @ B )
     => ( ( eq @ A @ C )
       => ( ( eq @ B @ D )
         => ( lessf @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(16,plain,
    ! [A: frac,B: frac] :
      ( ( lessf @ A @ B )
     => ! [C: frac] :
          ( ( eq @ A @ C )
         => ! [D: frac] :
              ( ( eq @ B @ D )
             => ( lessf @ C @ D ) ) ) ),
    inference(miniscope,[status(thm)],[15]) ).

thf(17,plain,
    ! [D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ A @ B )
      | ~ ( eq @ A @ C )
      | ~ ( eq @ B @ D )
      | ( lessf @ C @ D ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(31,plain,
    ! [E: frac,D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ B @ C )
      | ~ ( eq @ B @ D )
      | ( lessf @ D @ E )
      | ( ( eq @ A @ A )
       != ( eq @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[24,17]) ).

thf(32,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ B @ A )
      | ~ ( eq @ B @ C )
      | ( lessf @ C @ A ) ),
    inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).

thf(39,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ B @ A )
      | ~ ( eq @ B @ C )
      | ( lessf @ C @ A ) ),
    inference(simp,[status(thm)],[32]) ).

thf(308,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( lessf @ B @ A )
      | ( lessf @ C @ A )
      | ( ( eq @ y @ x )
       != ( eq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[207,39]) ).

thf(309,plain,
    ! [A: frac] :
      ( ~ ( lessf @ y @ A )
      | ( lessf @ x @ A ) ),
    inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( x ))]]) ).

thf(1128,plain,
    ! [A: frac] :
      ( ( lessf @ x @ A )
      | ( ( lessf @ y @ z )
       != ( lessf @ y @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[13,309]) ).

thf(1129,plain,
    lessf @ x @ z,
    inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( z ))]]) ).

thf(1141,plain,
    $false,
    inference(rewrite,[status(thm)],[1129,10]) ).

thf(1142,plain,
    $false,
    inference(simp,[status(thm)],[1141]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : NUM742^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n013.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May 20 05:25:39 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 1.17/1.11  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.51/1.29  % [INFO] 	 Parsing done (184ms). 
% 1.51/1.31  % [INFO] 	 Running in sequential loop mode. 
% 2.12/1.73  % [INFO] 	 nitpick registered as external prover. 
% 2.12/1.74  % [INFO] 	 Scanning for conjecture ... 
% 2.40/1.82  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 2.43/1.86  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 2.43/1.89  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.43/1.89  % [INFO] 	 Type checking passed. 
% 2.43/1.90  % [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 ... 
% 13.29/4.07  % [INFO] 	 Killing All external provers ... 
% 13.29/4.08  % Time passed: 3533ms (effective reasoning time: 2763ms)
% 13.29/4.08  % 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)>
% 13.29/4.08  % Axioms used in derivation (6): satz50, satz37, l, satz45, satz38, k
% 13.29/4.08  % No. of inferences in proof: 39
% 13.29/4.08  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3533 ms resp. 2763 ms w/o parsing
% 13.29/4.14  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.29/4.14  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------