TSTP Solution File: NUM739^1 by Leo-III-SAT---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM739^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 10:45:27 EDT 2024

% Result   : Theorem 21.79s 4.31s
% Output   : Refutation 21.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   72 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :  173 (  15 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  450 (  68   ~;  56   |;   0   &; 304   @)
%                                         (   0 <=>;  22  =>;   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     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :   82 (   0   ^  82   !;   0   ?;  82   :)

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

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

thf(4,axiom,
    eq @ x @ z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).

thf(15,plain,
    eq @ x @ z,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [A: frac,B: frac] :
      ( ( eq @ A @ B )
     => ( eq @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).

thf(21,plain,
    ! [A: frac,B: frac] :
      ( ( eq @ A @ B )
     => ( eq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

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

thf(189,plain,
    ! [B: frac,A: frac] :
      ( ( eq @ B @ A )
      | ( ( eq @ x @ z )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[15,22]) ).

thf(190,plain,
    eq @ z @ x,
    inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).

thf(7,axiom,
    ! [A: frac,B: frac,C: frac] :
      ( ( eq @ A @ B )
     => ( ( eq @ B @ C )
       => ( eq @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).

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

thf(19,plain,
    ! [A: frac,B: frac] :
      ( ( eq @ A @ B )
     => ! [C: frac] :
          ( ( eq @ B @ C )
         => ( eq @ A @ C ) ) ),
    inference(miniscope,[status(thm)],[18]) ).

thf(20,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ~ ( eq @ B @ C )
      | ( eq @ A @ C ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(50,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( eq @ B @ C )
      | ( eq @ A @ C )
      | ( ( eq @ x @ z )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[15,20]) ).

thf(51,plain,
    ! [A: frac] :
      ( ~ ( eq @ z @ A )
      | ( eq @ x @ A ) ),
    inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).

thf(57,plain,
    ! [A: frac] :
      ( ~ ( eq @ z @ A )
      | ( eq @ x @ A ) ),
    inference(simp,[status(thm)],[51]) ).

thf(689,plain,
    ! [A: frac] :
      ( ( eq @ x @ A )
      | ( ( eq @ z @ x )
       != ( eq @ z @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[190,57]) ).

thf(690,plain,
    eq @ x @ x,
    inference(pattern_uni,[status(thm)],[689:[bind(A,$thf( x ))]]) ).

thf(5,axiom,
    eq @ y @ u,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).

thf(16,plain,
    eq @ y @ u,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ! [A: frac,B: frac,C: frac,D: frac] :
      ( ( moref @ A @ B )
     => ( ( eq @ A @ C )
       => ( ( eq @ B @ D )
         => ( moref @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).

thf(23,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)],[9]) ).

thf(24,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)],[23]) ).

thf(25,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)],[24]) ).

thf(297,plain,
    ! [D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( moref @ A @ B )
      | ~ ( eq @ A @ C )
      | ( moref @ C @ D )
      | ( ( eq @ y @ u )
       != ( eq @ B @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[16,25]) ).

thf(298,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ y )
      | ~ ( eq @ A @ B )
      | ( moref @ B @ u ) ),
    inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( C )),bind(D,$thf( u ))]]) ).

thf(323,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ y )
      | ~ ( eq @ A @ B )
      | ( moref @ B @ u ) ),
    inference(simp,[status(thm)],[298]) ).

thf(4677,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ y )
      | ( moref @ B @ u )
      | ( ( eq @ x @ x )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[690,323]) ).

thf(4678,plain,
    ( ~ ( moref @ x @ y )
    | ( moref @ x @ u ) ),
    inference(pattern_uni,[status(thm)],[4677:[bind(A,$thf( x )),bind(B,$thf( x ))]]) ).

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

thf(13,plain,
    ( ~ ( moref @ x @ y )
   => ( eq @ x @ y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    ( ( moref @ x @ y )
    | ( eq @ x @ y ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(46,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( eq @ A @ C )
      | ( ( eq @ y @ u )
       != ( eq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[16,20]) ).

thf(47,plain,
    ! [A: frac] :
      ( ~ ( eq @ A @ y )
      | ( eq @ A @ u ) ),
    inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( u ))]]) ).

thf(62,plain,
    ! [A: frac] :
      ( ( moref @ x @ y )
      | ( eq @ A @ u )
      | ( ( eq @ x @ y )
       != ( eq @ A @ y ) ) ),
    inference(paramod_ordered,[status(thm)],[14,47]) ).

thf(63,plain,
    ( ( moref @ x @ y )
    | ( eq @ x @ u ) ),
    inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( x ))]]) ).

thf(1,conjecture,
    ( ~ ( moref @ z @ u )
   => ( eq @ z @ u ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz46) ).

thf(2,negated_conjecture,
    ~ ( ~ ( moref @ z @ u )
     => ( eq @ z @ u ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ( ~ ( moref @ z @ u )
     => ( eq @ z @ u ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    ~ ( eq @ z @ u ),
    inference(cnf,[status(esa)],[10]) ).

thf(48,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ~ ( eq @ B @ C )
      | ( ( eq @ A @ C )
       != ( eq @ z @ u ) ) ),
    inference(paramod_ordered,[status(thm)],[20,11]) ).

thf(49,plain,
    ! [A: frac] :
      ( ~ ( eq @ z @ A )
      | ~ ( eq @ A @ u ) ),
    inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( z )),bind(B,$thf( B )),bind(C,$thf( u ))]]) ).

thf(56,plain,
    ! [A: frac] :
      ( ~ ( eq @ z @ A )
      | ~ ( eq @ A @ u ) ),
    inference(simp,[status(thm)],[49]) ).

thf(236,plain,
    ! [A: frac] :
      ( ~ ( eq @ A @ u )
      | ( ( eq @ z @ x )
       != ( eq @ z @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[190,56]) ).

thf(237,plain,
    ~ ( eq @ x @ u ),
    inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( x ))]]) ).

thf(259,plain,
    ( ( moref @ x @ y )
    | $false ),
    inference(rewrite,[status(thm)],[63,237]) ).

thf(260,plain,
    moref @ x @ y,
    inference(simp,[status(thm)],[259]) ).

thf(178,plain,
    ! [B: frac,A: frac] :
      ( ( eq @ B @ A )
      | ( ( eq @ y @ u )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[16,22]) ).

thf(179,plain,
    eq @ u @ y,
    inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( y )),bind(B,$thf( u ))]]) ).

thf(288,plain,
    ! [D: frac,C: frac,B: frac,A: frac] :
      ( ~ ( moref @ A @ B )
      | ~ ( eq @ A @ C )
      | ( moref @ C @ D )
      | ( ( eq @ u @ y )
       != ( eq @ B @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[179,25]) ).

thf(289,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ u )
      | ~ ( eq @ A @ B )
      | ( moref @ B @ y ) ),
    inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( A )),bind(B,$thf( u )),bind(C,$thf( C )),bind(D,$thf( y ))]]) ).

thf(319,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ u )
      | ~ ( eq @ A @ B )
      | ( moref @ B @ y ) ),
    inference(simp,[status(thm)],[289]) ).

thf(4267,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ u )
      | ( moref @ B @ y )
      | ( ( eq @ x @ z )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[15,319]) ).

thf(4268,plain,
    ( ~ ( moref @ x @ u )
    | ( moref @ z @ y ) ),
    inference(pattern_uni,[status(thm)],[4267:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).

thf(52,plain,
    ! [C: frac,B: frac,A: frac] :
      ( ~ ( eq @ A @ B )
      | ( eq @ A @ C )
      | ( ( eq @ x @ z )
       != ( eq @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[15,20]) ).

thf(53,plain,
    ! [A: frac] :
      ( ~ ( eq @ A @ x )
      | ( eq @ A @ z ) ),
    inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( A )),bind(B,$thf( x )),bind(C,$thf( z ))]]) ).

thf(566,plain,
    ! [A: frac] :
      ( ( eq @ A @ z )
      | ( ( eq @ z @ x )
       != ( eq @ A @ x ) ) ),
    inference(paramod_ordered,[status(thm)],[190,53]) ).

thf(567,plain,
    eq @ z @ z,
    inference(pattern_uni,[status(thm)],[566:[bind(A,$thf( z ))]]) ).

thf(4675,plain,
    ! [B: frac,A: frac] :
      ( ~ ( moref @ A @ y )
      | ( moref @ B @ u )
      | ( ( eq @ z @ z )
       != ( eq @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[567,323]) ).

thf(4676,plain,
    ( ~ ( moref @ z @ y )
    | ( moref @ z @ u ) ),
    inference(pattern_uni,[status(thm)],[4675:[bind(A,$thf( z )),bind(B,$thf( z ))]]) ).

thf(12,plain,
    ~ ( moref @ z @ u ),
    inference(cnf,[status(esa)],[10]) ).

thf(7063,plain,
    ( ~ ( moref @ z @ y )
    | $false ),
    inference(rewrite,[status(thm)],[4676,12]) ).

thf(7064,plain,
    ~ ( moref @ z @ y ),
    inference(simp,[status(thm)],[7063]) ).

thf(7065,plain,
    ( ~ ( moref @ x @ u )
    | $false ),
    inference(rewrite,[status(thm)],[4268,7064]) ).

thf(7066,plain,
    ~ ( moref @ x @ u ),
    inference(simp,[status(thm)],[7065]) ).

thf(7207,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[4678,260,7066]) ).

thf(7208,plain,
    $false,
    inference(simp,[status(thm)],[7207]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : NUM739^1 : TPTP v8.1.2. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.34  % Computer : n023.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Mon May  6 19:50:39 EDT 2024
% 0.15/0.34  % CPUTime  : 
% 0.87/0.77  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.11/0.88  % [INFO] 	 Parsing done (107ms). 
% 1.11/0.89  % [INFO] 	 Running in sequential loop mode. 
% 1.51/1.08  % [INFO] 	 nitpick registered as external prover. 
% 1.51/1.08  % [INFO] 	 Scanning for conjecture ... 
% 1.51/1.13  % [INFO] 	 Found a conjecture and 7 axioms. Running axiom selection ... 
% 1.68/1.15  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.68/1.16  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.68/1.16  % [INFO] 	 Type checking passed. 
% 1.68/1.17  % [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 ... 
% 21.79/4.30  % [INFO] 	 Killing All external provers ... 
% 21.79/4.31  % Time passed: 3799ms (effective reasoning time: 3416ms)
% 21.79/4.31  % 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)>
% 21.79/4.31  % Axioms used in derivation (6): e, f, satz39, m, satz44, satz38
% 21.79/4.31  % No. of inferences in proof: 65
% 21.79/4.31  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3799 ms resp. 3416 ms w/o parsing
% 21.97/4.40  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.97/4.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------