%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL106-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 : Fri May 19 11:29:23 EDT 2023

% Result   : Unsatisfiable 2.34s 1.52s
% Output   : Refutation 2.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   14 (   7 unt;   5 typ;   0 def)
%            Number of atoms       :   13 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   86 (   6   ~;   4   |;   0   &;  76   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   16 (   0   ^;  16   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(is_a_theorem_type,type,
    is_a_theorem: $i > $o ).

thf(equivalent_type,type,
    equivalent: $i > $i > $i ).

thf(a_type,type,
    a: $i ).

thf(b_type,type,
    b: $i ).

thf(c_type,type,
    c: $i ).

thf(1,negated_conjecture,
    ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ b ) @ ( equivalent @ ( equivalent @ c @ a ) @ ( equivalent @ c @ b ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_q_2) ).

thf(5,plain,
    ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ a @ b ) @ ( equivalent @ ( equivalent @ c @ a ) @ ( equivalent @ c @ b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( is_a_theorem @ ( equivalent @ A @ B ) )
      | ~ ( is_a_theorem @ A )
      | ( is_a_theorem @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( is_a_theorem @ ( equivalent @ A @ B ) )
      | ~ ( is_a_theorem @ A )
      | ( is_a_theorem @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ ( equivalent @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_1) ).

thf(9,plain,
    ! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ A @ ( equivalent @ ( equivalent @ B @ C ) @ ( equivalent @ ( equivalent @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_4) ).

thf(10,plain,
    ! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(11,plain,
    $false,
    inference(e,[status(thm)],[5,7,9,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : LCL106-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n009.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 : Thu May 18 16:12:33 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.97  % [INFO] 	 Parsing done (105ms). 
% 1.20/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.48/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.68/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.23  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.86/1.25  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.86/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.86/1.26  % [INFO] 	 Type checking passed. 
% 1.86/1.26  % [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 ... 
% 2.34/1.52  % External prover 'e' found a proof!
% 2.34/1.52  % [INFO] 	 Killing All external provers ... 
% 2.34/1.52  % Time passed: 989ms (effective reasoning time: 539ms)
% 2.34/1.52  % 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)>
% 2.34/1.52  % Axioms used in derivation (3): condensed_detachment, q_1, q_4
% 2.34/1.52  % No. of inferences in proof: 9
% 2.34/1.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 989 ms resp. 539 ms w/o parsing
% 2.64/1.56  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.64/1.56  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------