%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PUZ024-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 0.20s 0.34s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   20 (  12 unt;   4 nHn;  17 RR)
%            Number of literals    :   35 (   0 equ;  18 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   26 (  13 sgn)

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

cnf(liars_lie,axiom,
    ( ~ a_truth(liar(Liar))
    | ~ a_truth(says(Liar,Statement))
    | ~ a_truth(Statement) ) ).

cnf(all_truthtellers,axiom,
    ( a_truth(all_are_liars)
    | ~ people(X,Y,Z)
    | a_truth(truthteller(X))
    | a_truth(truthteller(Y))
    | a_truth(truthteller(Z)) ) ).

cnf(a_c_b_people,hypothesis,
    people(a,c,b) ).

cnf(a_says_all_are_liars,hypothesis,
    a_truth(says(a,all_are_liars)) ).

cnf(prove_there_is_a_truthteller,negated_conjecture,
    ~ a_truth(truthteller(Truthteller)) ).

cnf(refute_0_0,plain,
    ~ a_truth(truthteller(X)),
    inference(subst,[],[prove_there_is_a_truthteller:[bind(Truthteller,$fot(X))]]) ).

cnf(refute_0_1,plain,
    a_truth(liar(X)),
    inference(resolve,[$cnf( a_truth(truthteller(X)) )],[truthteller_or_liar,refute_0_0]) ).

cnf(refute_0_2,plain,
    a_truth(liar(Liar)),
    inference(subst,[],[refute_0_1:[bind(X,$fot(Liar))]]) ).

cnf(refute_0_3,plain,
    ( ~ a_truth(Statement)
    | ~ a_truth(says(Liar,Statement)) ),
    inference(resolve,[$cnf( a_truth(liar(Liar)) )],[refute_0_2,liars_lie]) ).

cnf(refute_0_4,plain,
    ( ~ a_truth(all_are_liars)
    | ~ a_truth(says(a,all_are_liars)) ),
    inference(subst,[],[refute_0_3:[bind(Liar,$fot(a)),bind(Statement,$fot(all_are_liars))]]) ).

cnf(refute_0_5,plain,
    ~ a_truth(all_are_liars),
    inference(resolve,[$cnf( a_truth(says(a,all_are_liars)) )],[a_says_all_are_liars,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ people(X,Y,Z)
    | a_truth(truthteller(X))
    | a_truth(truthteller(Y))
    | a_truth(truthteller(Z)) ),
    inference(resolve,[$cnf( a_truth(all_are_liars) )],[all_truthtellers,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ people(X,Y,Z)
    | a_truth(truthteller(Y))
    | a_truth(truthteller(Z)) ),
    inference(resolve,[$cnf( a_truth(truthteller(X)) )],[refute_0_6,refute_0_0]) ).

cnf(refute_0_8,plain,
    ~ a_truth(truthteller(Y)),
    inference(subst,[],[prove_there_is_a_truthteller:[bind(Truthteller,$fot(Y))]]) ).

cnf(refute_0_9,plain,
    ( ~ people(X,Y,Z)
    | a_truth(truthteller(Z)) ),
    inference(resolve,[$cnf( a_truth(truthteller(Y)) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ a_truth(truthteller(Z)),
    inference(subst,[],[prove_there_is_a_truthteller:[bind(Truthteller,$fot(Z))]]) ).

cnf(refute_0_11,plain,
    ~ people(X,Y,Z),
    inference(resolve,[$cnf( a_truth(truthteller(Z)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ~ people(a,c,b),
    inference(subst,[],[refute_0_11:[bind(X,$fot(a)),bind(Y,$fot(c)),bind(Z,$fot(b))]]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( people(a,c,b) )],[a_c_b_people,refute_0_12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : PUZ024-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n026.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun May 29 01:32:39 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.34  
% 0.20/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.34  
%------------------------------------------------------------------------------