TSTP Solution File: NUM754^1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM754^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 5.34s 2.14s
% Output   : Refutation 5.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   36 (  12 unt;   8 typ;   0 def)
%            Number of atoms       :   69 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  262 (  25   ~;  18   |;   0   &; 204   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   54 (   0   ^  54   !;   0   ?;  54   :)

% 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(u_type,type,
    u: frac ).

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

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

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

thf(3,axiom,
    eq @ x @ y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).

thf(9,plain,
    eq @ x @ y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    moref @ z @ u,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).

thf(10,plain,
    moref @ z @ u,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: frac,B: frac,C: frac,D: frac] :
      ( ( eq @ A @ B )
     => ( ( moref @ C @ D )
       => ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62g) ).

thf(14,plain,
    ! [A: frac,B: frac,C: frac,D: frac] :
      ( ( eq @ A @ B )
     => ( ( moref @ C @ D )
       => ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(15,plain,
    ! [A: frac,B: frac] :
      ( ( eq @ A @ B )
     => ! [C: frac,D: frac] :
          ( ( moref @ C @ D )
         => ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
    inference(miniscope,[status(thm)],[14]) ).

thf(16,plain,
    ! [D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ~ ( moref @ C @ D )
      | ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(76,plain,
    ! [D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
      | ( ( moref @ z @ u )
       != ( moref @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[10,16]) ).

thf(77,plain,
    ! [B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( moref @ ( pf @ A @ z ) @ ( pf @ B @ u ) ) ),
    inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).

thf(128,plain,
    ! [B: frac,A: frac] :
      ( ( moref @ ( pf @ A @ z ) @ ( pf @ B @ u ) )
      | ( ( eq @ x @ y )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9,77]) ).

thf(129,plain,
    moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
    inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).

thf(5,axiom,
    ! [A: frac,B: frac,C: frac,D: frac] :
      ( ( moref @ A @ B )
     => ( ( eq @ A @ C )
       => ( ( eq @ B @ D )
         => ( moref @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).

thf(11,plain,
    ! [A: frac,B: frac,C: frac,D: frac] :
      ( ( moref @ A @ B )
     => ( ( eq @ A @ C )
       => ( ( eq @ B @ D )
         => ( moref @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,plain,
    ! [A: frac,B: frac] :
      ( ( moref @ A @ B )
     => ! [C: frac] :
          ( ( eq @ A @ C )
         => ! [D: frac] :
              ( ( eq @ B @ D )
             => ( moref @ C @ D ) ) ) ),
    inference(miniscope,[status(thm)],[11]) ).

thf(13,plain,
    ! [D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( moref @ A @ B )
      | ~ ( eq @ A @ C )
      | ~ ( eq @ B @ D )
      | ( moref @ C @ D ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(1,conjecture,
    moref @ ( pf @ z @ x ) @ ( pf @ u @ y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62h) ).

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

thf(8,plain,
    ~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(33,plain,
    ! [D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( moref @ A @ B )
      | ~ ( eq @ A @ C )
      | ~ ( eq @ B @ D )
      | ( ( moref @ C @ D )
       != ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13,8]) ).

thf(34,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ B )
      | ~ ( eq @ A @ ( pf @ z @ x ) )
      | ~ ( eq @ B @ ( pf @ u @ y ) ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( pf @ z @ x )),bind(D,$thf( pf @ u @ y ))]]) ).

thf(210,plain,
    ! [B: frac,A: frac] :
      ( ~ ( eq @ A @ ( pf @ z @ x ) )
      | ~ ( eq @ B @ ( pf @ u @ y ) )
      | ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
       != ( moref @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[129,34]) ).

thf(211,plain,
    ( ~ ( eq @ ( pf @ x @ z ) @ ( pf @ z @ x ) )
    | ~ ( eq @ ( pf @ y @ u ) @ ( pf @ u @ y ) ) ),
    inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ y @ u ))]]) ).

thf(7,axiom,
    ! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58) ).

thf(17,plain,
    ! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(18,plain,
    ! [B: frac,A: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(263,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[211,18]) ).

thf(264,plain,
    $false,
    inference(simp,[status(thm)],[263]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM754^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n008.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May  6 19:42:54 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.88/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.96  % [INFO] 	 Parsing done (113ms). 
% 1.18/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.48/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.67/1.22  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.79/1.24  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.79/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.79/1.26  % [INFO] 	 Type checking passed. 
% 1.79/1.26  % [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 ... 
% 5.34/2.14  % [INFO] 	 Killing All external provers ... 
% 5.34/2.14  % Time passed: 1612ms (effective reasoning time: 1164ms)
% 5.34/2.14  % 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)>
% 5.34/2.14  % Axioms used in derivation (5): e, satz62g, satz44, m, satz58
% 5.34/2.14  % No. of inferences in proof: 28
% 5.34/2.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1612 ms resp. 1164 ms w/o parsing
% 5.34/2.17  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.34/2.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------