TSTP Solution File: LCL172-1 by Leo-III-SAT---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : LCL172-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 10:40:14 EDT 2024

% Result   : Unsatisfiable 17.88s 3.82s
% Output   : Refutation 17.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   37 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :   60 (   5 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  381 (  29   ~;  20   |;   0   &; 332   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   53 (   0   ^  53   !;   0   ?;  53   :)

% Comments : 
%------------------------------------------------------------------------------
thf(theorem_type,type,
    theorem: $i > $o ).

thf(or_type,type,
    or: $i > $i > $i ).

thf(not_type,type,
    not: $i > $i ).

thf(p_type,type,
    p: $i ).

thf(q_type,type,
    q: $i ).

thf(r_type,type,
    r: $i ).

thf(axiom_type,type,
    axiom: $i > $o ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ A ) @ B ) )
      | ~ ( axiom @ ( or @ ( not @ A ) @ C ) )
      | ~ ( theorem @ ( or @ ( not @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).

thf(21,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ A ) @ B ) )
      | ~ ( axiom @ ( or @ ( not @ A ) @ C ) )
      | ~ ( theorem @ ( or @ ( not @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ A ) @ B ) )
      | ~ ( axiom @ ( or @ ( not @ A ) @ C ) )
      | ~ ( theorem @ ( or @ ( not @ C ) @ B ) ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(1,negated_conjecture,
    ~ ( theorem @ ( or @ ( not @ ( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) ) ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(10,plain,
    ~ ( theorem @ ( or @ ( not @ ( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) ) ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(11,plain,
    ~ ( theorem @ ( or @ ( not @ ( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) ) ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) ),
    inference(polarity_switch,[status(thm)],[10]) ).

thf(42,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( axiom @ ( or @ ( not @ A ) @ C ) )
      | ~ ( theorem @ ( or @ ( not @ C ) @ B ) )
      | ( ( theorem @ ( or @ ( not @ A ) @ B ) )
       != ( theorem @ ( or @ ( not @ ( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) ) ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[22,11]) ).

thf(43,plain,
    ! [A: $i] :
      ( ~ ( axiom @ ( or @ ( not @ ( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) ) ) @ A ) )
      | ~ ( theorem @ ( or @ ( not @ A ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) )),bind(B,$thf( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) )),bind(C,$thf( C ))]]) ).

thf(48,plain,
    ! [A: $i] :
      ( ~ ( axiom @ ( or @ ( not @ ( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) ) ) @ A ) )
      | ~ ( theorem @ ( or @ ( not @ A ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) ) ),
    inference(simp,[status(thm)],[43]) ).

thf(62,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( theorem @ ( or @ ( not @ D ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) )
      | ( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
       != ( axiom @ ( or @ ( not @ ( or @ ( not @ p ) @ ( or @ ( not @ q ) @ r ) ) ) @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[15,48]) ).

thf(63,plain,
    ~ ( theorem @ ( or @ ( not @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) @ ( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ) ) ),
    inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( not @ p )),bind(B,$thf( not @ q )),bind(C,$thf( r )),bind(D,$thf( or @ ( not @ q ) @ ( or @ ( not @ p ) @ r ) ))]]) ).

thf(2,axiom,
    ! [A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).

thf(12,plain,
    ! [A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( theorem @ A )
      | ~ ( axiom @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).

thf(17,plain,
    ! [A: $i] :
      ( ( theorem @ A )
      | ~ ( axiom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(18,plain,
    ! [A: $i] :
      ( ( theorem @ A )
      | ~ ( axiom @ A ) ),
    inference(cnf,[status(esa)],[17]) ).

thf(92,plain,
    ! [B: $i,A: $i] :
      ( ( theorem @ B )
      | ( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
       != ( axiom @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,18]) ).

thf(93,plain,
    ! [A: $i] : ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
    inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( D )),bind(B,$thf( or @ ( not @ ( or @ D @ D ) ) @ D ))]]) ).

thf(101,plain,
    ! [A: $i] : ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ),
    inference(simp,[status(thm)],[93]) ).

thf(3,axiom,
    ! [B: $i,A: $i] : ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).

thf(13,plain,
    ! [B: $i,A: $i] : ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(36,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ C ) @ D ) )
      | ~ ( theorem @ ( or @ ( not @ E ) @ D ) )
      | ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
       != ( axiom @ ( or @ ( not @ C ) @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13,22]) ).

thf(37,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ C ) @ A ) )
      | ~ ( theorem @ ( or @ ( not @ ( or @ B @ C ) ) @ A ) ) ),
    inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( or @ F @ G ))]]) ).

thf(46,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ C ) @ A ) )
      | ~ ( theorem @ ( or @ ( not @ ( or @ B @ C ) ) @ A ) ) ),
    inference(simp,[status(thm)],[37]) ).

thf(1654,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ D ) @ B ) )
      | ( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
       != ( theorem @ ( or @ ( not @ ( or @ C @ D ) ) @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[101,46]) ).

thf(1655,plain,
    ! [A: $i] : ( theorem @ ( or @ ( not @ A ) @ A ) ),
    inference(pattern_uni,[status(thm)],[1654:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(1695,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[63,1655]) ).

thf(1696,plain,
    $false,
    inference(simp,[status(thm)],[1695]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL172-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n020.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 19:09:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.12/0.99  % [INFO] 	 Parsing done (112ms). 
% 1.12/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.25  % [INFO] 	 Found a conjecture and 8 axioms. Running axiom selection ... 
% 1.80/1.27  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.80/1.28  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.80/1.28  % [INFO] 	 Type checking passed. 
% 1.80/1.29  % [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 ... 
% 17.88/3.80  % [INFO] 	 Killing All external provers ... 
% 17.88/3.81  % Time passed: 3261ms (effective reasoning time: 2811ms)
% 17.88/3.81  % 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)>
% 17.88/3.82  % Axioms used in derivation (5): axiom_1_5, rule_1, axiom_1_3, rule_3, axiom_1_2
% 17.88/3.82  % No. of inferences in proof: 30
% 17.88/3.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3261 ms resp. 2811 ms w/o parsing
% 17.88/3.89  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.88/3.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------