%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% 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  : 600s
% DateTime : Sat Jul 16 05:23:29 EDT 2022

% Result   : Unsatisfiable 0.18s 0.48s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   25 (  11 unt;   3 nHn;  24 RR)
%            Number of literals    :   44 (  20 equ;  21 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   11 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(t1,axiom,
    ( ~ between(U,V,W)
    | between(W,V,U) ) ).

cnf(b2,axiom,
    ( ~ between(U,V,W)
    | ~ between(V,U,W)
    | U = V ) ).

cnf(a_not_c,hypothesis,
    a != c ).

cnf(c_not_d,hypothesis,
    c != d ).

cnf(c_between_a_and_d,hypothesis,
    between(a,c,d) ).

cnf(prove_not_between_others,negated_conjecture,
    ( between(c,a,d)
    | between(a,d,c) ) ).

cnf(refute_0_0,plain,
    ( ~ between(a,d,c)
    | between(c,d,a) ),
    inference(subst,[],[t1:[bind(U,$fot(a)),bind(V,$fot(d)),bind(W,$fot(c))]]) ).

cnf(refute_0_1,plain,
    ( ~ between(a,c,d)
    | ~ between(c,a,d)
    | c = a ),
    inference(subst,[],[b2:[bind(U,$fot(c)),bind(V,$fot(a)),bind(W,$fot(d))]]) ).

cnf(refute_0_2,plain,
    ( ~ between(a,c,d)
    | c = a
    | between(a,d,c) ),
    inference(resolve,[$cnf( between(c,a,d) )],[prove_not_between_others,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( c = a
    | between(a,d,c) ),
    inference(resolve,[$cnf( between(a,c,d) )],[c_between_a_and_d,refute_0_2]) ).

cnf(refute_0_4,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_5,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_6,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( c != a
    | a = c ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(c)),bind(Y,$fot(a))]]) ).

cnf(refute_0_8,plain,
    c != a,
    inference(resolve,[$cnf( $equal(a,c) )],[refute_0_7,a_not_c]) ).

cnf(refute_0_9,plain,
    between(a,d,c),
    inference(resolve,[$cnf( $equal(c,a) )],[refute_0_3,refute_0_8]) ).

cnf(refute_0_10,plain,
    between(c,d,a),
    inference(resolve,[$cnf( between(a,d,c) )],[refute_0_9,refute_0_0]) ).

cnf(refute_0_11,plain,
    ( ~ between(a,c,d)
    | between(d,c,a) ),
    inference(subst,[],[t1:[bind(U,$fot(a)),bind(V,$fot(c)),bind(W,$fot(d))]]) ).

cnf(refute_0_12,plain,
    between(d,c,a),
    inference(resolve,[$cnf( between(a,c,d) )],[c_between_a_and_d,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ between(c,d,a)
    | ~ between(d,c,a)
    | d = c ),
    inference(subst,[],[b2:[bind(U,$fot(d)),bind(V,$fot(c)),bind(W,$fot(a))]]) ).

cnf(refute_0_14,plain,
    ( ~ between(c,d,a)
    | d = c ),
    inference(resolve,[$cnf( between(d,c,a) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( d != c
    | c = d ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(d)),bind(Y,$fot(c))]]) ).

cnf(refute_0_16,plain,
    d != c,
    inference(resolve,[$cnf( $equal(c,d) )],[refute_0_15,c_not_d]) ).

cnf(refute_0_17,plain,
    ~ between(c,d,a),
    inference(resolve,[$cnf( $equal(d,c) )],[refute_0_14,refute_0_16]) ).

cnf(refute_0_18,plain,
    $false,
    inference(resolve,[$cnf( between(c,d,a) )],[refute_0_10,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GEO006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n021.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 Jun 18 14:34:01 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.48  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48  
% 0.18/0.48  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.48  
%------------------------------------------------------------------------------