TSTP Solution File: LCL171-3 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL171-3 : TPTP v8.2.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 00:09:17 EDT 2024

% Result   : Unsatisfiable 8.47s 3.04s
% Output   : Refutation 8.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   29 (  16 unt;   7 typ;   0 def)
%            Number of atoms       :   30 (   6 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  160 (  10   ~;   6   |;   0   &; 144   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   36 (   0   ^  36   !;   0   ?;  36   :)

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

thf(implies_type,type,
    implies: $i > $i > $i ).

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

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

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

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

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

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

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

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

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( implies @ A @ B )
      = ( or @ ( not @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( implies @ A @ B )
      = ( or @ ( not @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ( or @ ( not @ A ) @ B )
      = ( implies @ A @ B ) ),
    inference(lifteq,[status(thm)],[17]) ).

thf(4,axiom,
    ! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).

thf(14,plain,
    ! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( theorem @ A )
      | ~ ( axiom @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).

thf(19,plain,
    ! [A: $i] :
      ( ( theorem @ A )
      | ~ ( axiom @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(20,plain,
    ! [A: $i] :
      ( ( theorem @ A )
      | ~ ( axiom @ A ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(52,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( theorem @ C )
      | ( ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
       != ( axiom @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[14,20]) ).

thf(53,plain,
    ! [B: $i,A: $i] : ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) ),
    inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( implies @ ( or @ I @ H ) @ ( or @ H @ I ) ))]]) ).

thf(58,plain,
    ! [B: $i,A: $i] : ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) ),
    inference(simp,[status(thm)],[53]) ).

thf(139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( theorem @ ( implies @ ( implies @ A @ B ) @ ( or @ C @ D ) ) )
      | ( ( or @ ( not @ A ) @ B )
       != ( or @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[18,58]) ).

thf(140,plain,
    ! [B: $i,A: $i] : ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).

thf(147,plain,
    ! [B: $i,A: $i] : ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) ),
    inference(simp,[status(thm)],[140]) ).

thf(190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( theorem @ ( implies @ ( implies @ D @ C ) @ ( implies @ A @ B ) ) )
      | ( ( or @ ( not @ A ) @ B )
       != ( or @ C @ ( not @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[18,147]) ).

thf(191,plain,
    ! [B: $i,A: $i] : ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) ),
    inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).

thf(199,plain,
    ! [B: $i,A: $i] : ( theorem @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) ),
    inference(simp,[status(thm)],[191]) ).

thf(272,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[11,199]) ).

thf(273,plain,
    $false,
    inference(simp,[status(thm)],[272]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : LCL171-3 : TPTP v8.2.0. Released v2.3.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n021.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 03:28:39 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.92/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/1.05  % [INFO] 	 Parsing done (156ms). 
% 1.20/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.41  % [INFO] 	 nitpick registered as external prover. 
% 1.74/1.42  % [INFO] 	 Scanning for conjecture ... 
% 1.97/1.50  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 2.04/1.53  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.04/1.54  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.04/1.55  % [INFO] 	 Type checking passed. 
% 2.04/1.55  % [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 ... 
% 8.47/3.03  % [INFO] 	 Killing All external provers ... 
% 8.47/3.03  % Time passed: 2576ms (effective reasoning time: 1959ms)
% 8.47/3.04  % Axioms used in derivation (3): implies_definition, axiom_1_4, rule_1
% 8.47/3.04  % No. of inferences in proof: 22
% 8.47/3.04  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2576 ms resp. 1959 ms w/o parsing
% 8.47/3.07  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.47/3.07  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------