%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PUZ023-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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  : 600s
% DateTime : Mon Jul 18 18:20:38 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   24 (   9 unt;   4 nHn;  23 RR)
%            Number of literals    :   43 (   0 equ;  25 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-1 aty)
%            Number of variables   :    2 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(truthteller_or_liar,axiom,
    ( a_truth(truthteller(X))
    | a_truth(liar(X)) ) ).

cnf(b_and_c_liars,hypothesis,
    ( ~ a_truth(liar(b))
    | ~ a_truth(liar(c))
    | an_answer(b_and_c_liars) ) ).

cnf(b_liar_and_c_truthteller,hypothesis,
    ( ~ a_truth(liar(b))
    | ~ a_truth(truthteller(c))
    | an_answer(b_liar_and_c_truthteller) ) ).

cnf(b_truthteller_and_c_liar,hypothesis,
    ( ~ a_truth(truthteller(b))
    | ~ a_truth(liar(c))
    | an_answer(b_truthteller_and_c_liar) ) ).

cnf(b_and_c_truthtellers,hypothesis,
    ( ~ a_truth(truthteller(b))
    | ~ a_truth(truthteller(c))
    | an_answer(b_and_c_truthtellers) ) ).

cnf(prove_there_is_an_answer,negated_conjecture,
    ~ an_answer(X) ).

cnf(refute_0_0,plain,
    ~ an_answer(b_and_c_liars),
    inference(subst,[],[prove_there_is_an_answer:[bind(X,$fot(b_and_c_liars))]]) ).

cnf(refute_0_1,plain,
    ( ~ a_truth(liar(b))
    | ~ a_truth(liar(c)) ),
    inference(resolve,[$cnf( an_answer(b_and_c_liars) )],[b_and_c_liars,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( a_truth(liar(c))
    | a_truth(truthteller(c)) ),
    inference(subst,[],[truthteller_or_liar:[bind(X,$fot(c))]]) ).

cnf(refute_0_3,plain,
    ~ an_answer(b_liar_and_c_truthteller),
    inference(subst,[],[prove_there_is_an_answer:[bind(X,$fot(b_liar_and_c_truthteller))]]) ).

cnf(refute_0_4,plain,
    ( ~ a_truth(liar(b))
    | ~ a_truth(truthteller(c)) ),
    inference(resolve,[$cnf( an_answer(b_liar_and_c_truthteller) )],[b_liar_and_c_truthteller,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ a_truth(liar(b))
    | a_truth(liar(c)) ),
    inference(resolve,[$cnf( a_truth(truthteller(c)) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( a_truth(liar(b))
    | a_truth(truthteller(b)) ),
    inference(subst,[],[truthteller_or_liar:[bind(X,$fot(b))]]) ).

cnf(refute_0_7,plain,
    ~ an_answer(b_truthteller_and_c_liar),
    inference(subst,[],[prove_there_is_an_answer:[bind(X,$fot(b_truthteller_and_c_liar))]]) ).

cnf(refute_0_8,plain,
    ( ~ a_truth(liar(c))
    | ~ a_truth(truthteller(b)) ),
    inference(resolve,[$cnf( an_answer(b_truthteller_and_c_liar) )],[b_truthteller_and_c_liar,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ a_truth(liar(c))
    | a_truth(liar(b)) ),
    inference(resolve,[$cnf( a_truth(truthteller(b)) )],[refute_0_6,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ an_answer(b_and_c_truthtellers),
    inference(subst,[],[prove_there_is_an_answer:[bind(X,$fot(b_and_c_truthtellers))]]) ).

cnf(refute_0_11,plain,
    ( ~ a_truth(truthteller(b))
    | ~ a_truth(truthteller(c)) ),
    inference(resolve,[$cnf( an_answer(b_and_c_truthtellers) )],[b_and_c_truthtellers,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ a_truth(truthteller(b))
    | a_truth(liar(c)) ),
    inference(resolve,[$cnf( a_truth(truthteller(c)) )],[refute_0_2,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( a_truth(liar(b))
    | a_truth(liar(c)) ),
    inference(resolve,[$cnf( a_truth(truthteller(b)) )],[refute_0_6,refute_0_12]) ).

cnf(refute_0_14,plain,
    a_truth(liar(b)),
    inference(resolve,[$cnf( a_truth(liar(c)) )],[refute_0_13,refute_0_9]) ).

cnf(refute_0_15,plain,
    a_truth(liar(c)),
    inference(resolve,[$cnf( a_truth(liar(b)) )],[refute_0_14,refute_0_5]) ).

cnf(refute_0_16,plain,
    ~ a_truth(liar(b)),
    inference(resolve,[$cnf( a_truth(liar(c)) )],[refute_0_15,refute_0_1]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( a_truth(liar(b)) )],[refute_0_14,refute_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ023-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat May 28 21:46:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------