TSTP Solution File: LCL186-1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL186-1 : TPTP v8.2.0. Released v1.1.0.
% 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 21 00:09:21 EDT 2024

% Result   : Unsatisfiable 6.24s 2.68s
% Output   : Refutation 6.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   30 (  13 unt;   6 typ;   0 def)
%            Number of atoms       :   47 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  260 (  25   ~;  15   |;   0   &; 220   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (   0   ^  40   !;   0   ?;  40   :)

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

thf(4,axiom,
    ! [B: $i,A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).

thf(14,plain,
    ! [B: $i,A: $i] : ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( theorem @ A )
      | ~ ( axiom @ A ) ),
    file('/export/starexec/sandbox2/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(78,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ C )
      | ( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
       != ( axiom @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[14,18]) ).

thf(79,plain,
    ! [B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( or @ ( not @ ( or @ J @ I ) ) @ ( or @ I @ J ) ))]]) ).

thf(92,plain,
    ! [B: $i,A: $i] : ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) ),
    inference(simp,[status(thm)],[79]) ).

thf(3,axiom,
    ! [B: $i,A: $i] : ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) ),
    file('/export/starexec/sandbox2/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(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/sandbox2/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 @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

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

thf(11,plain,
    ~ ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) ),
    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 @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[22,11]) ).

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

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

thf(56,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( theorem @ ( or @ ( not @ C ) @ ( or @ ( not @ p ) @ q ) ) )
      | ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
       != ( axiom @ ( or @ ( not @ ( not @ p ) ) @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13,48]) ).

thf(57,plain,
    ! [A: $i] :
      ~ ( theorem @ ( or @ ( not @ ( or @ A @ ( not @ p ) ) ) @ ( or @ ( not @ p ) @ q ) ) ),
    inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( not @ p )),bind(B,$thf( E )),bind(C,$thf( or @ E @ ( not @ p ) ))]]) ).

thf(65,plain,
    ! [A: $i] :
      ~ ( theorem @ ( or @ ( not @ ( or @ A @ ( not @ p ) ) ) @ ( or @ ( not @ p ) @ q ) ) ),
    inference(simp,[status(thm)],[57]) ).

thf(143,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) )
     != ( theorem @ ( or @ ( not @ ( or @ C @ ( not @ p ) ) ) @ ( or @ ( not @ p ) @ q ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,65]) ).

thf(144,plain,
    $false,
    inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( not @ p )),bind(B,$thf( q )),bind(C,$thf( q ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : LCL186-1 : TPTP v8.2.0. Released v1.1.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n008.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon May 20 01:54:09 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.94/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.08  % [INFO] 	 Parsing done (164ms). 
% 1.30/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.73/1.44  % [INFO] 	 nitpick registered as external prover. 
% 1.73/1.45  % [INFO] 	 Scanning for conjecture ... 
% 1.98/1.53  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 2.03/1.56  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.03/1.58  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.03/1.58  % [INFO] 	 Type checking passed. 
% 2.03/1.58  % [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 ... 
% 6.24/2.68  % [INFO] 	 Killing All external provers ... 
% 6.24/2.68  % Time passed: 2226ms (effective reasoning time: 1578ms)
% 6.24/2.68  % Axioms used in derivation (4): axiom_1_4, rule_1, axiom_1_3, rule_3
% 6.24/2.68  % No. of inferences in proof: 24
% 6.24/2.68  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2226 ms resp. 1578 ms w/o parsing
% 6.24/2.73  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.24/2.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------