%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO067-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 05:24:02 EDT 2022

% Result   : Unsatisfiable 0.18s 0.56s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   42 (  18 unt;   0 nHn;  33 RR)
%            Number of literals    :   80 (  17 equ;  44 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   33 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(colinearity1,axiom,
    ( ~ between(X,Y,Z)
    | colinear(X,Y,Z) ) ).

cnf(colinearity2,axiom,
    ( ~ between(Y,Z,X)
    | colinear(X,Y,Z) ) ).

cnf(t3,axiom,
    between(U,V,V) ).

cnf(t2,axiom,
    between(U,U,V) ).

cnf(part_1,negated_conjecture,
    ( ~ colinear(x,x,y)
    | ~ colinear(x,y,x)
    | ~ colinear(y,x,x)
    | x = y ) ).

cnf(part_2,negated_conjecture,
    ( ~ colinear(x,x,y)
    | ~ colinear(x,y,x)
    | ~ colinear(y,x,x)
    | ~ colinear(x,z,y) ) ).

cnf(refute_0_0,plain,
    between(X_269,X_271,X_271),
    inference(subst,[],[t3:[bind(U,$fot(X_269)),bind(V,$fot(X_271))]]) ).

cnf(refute_0_1,plain,
    ( ~ between(X_269,X_271,X_271)
    | colinear(X_269,X_271,X_271) ),
    inference(subst,[],[colinearity1:[bind(X,$fot(X_269)),bind(Y,$fot(X_271)),bind(Z,$fot(X_271))]]) ).

cnf(refute_0_2,plain,
    colinear(X_269,X_271,X_271),
    inference(resolve,[$cnf( between(X_269,X_271,X_271) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    colinear(y,x,x),
    inference(subst,[],[refute_0_2:[bind(X_269,$fot(y)),bind(X_271,$fot(x))]]) ).

cnf(refute_0_4,plain,
    ( ~ colinear(x,x,y)
    | ~ colinear(x,y,x)
    | x = y ),
    inference(resolve,[$cnf( colinear(y,x,x) )],[refute_0_3,part_1]) ).

cnf(refute_0_5,plain,
    between(X_270,X_270,X_271),
    inference(subst,[],[t2:[bind(U,$fot(X_270)),bind(V,$fot(X_271))]]) ).

cnf(refute_0_6,plain,
    ( ~ between(X_270,X_270,X_271)
    | colinear(X_270,X_270,X_271) ),
    inference(subst,[],[colinearity1:[bind(X,$fot(X_270)),bind(Y,$fot(X_270)),bind(Z,$fot(X_271))]]) ).

cnf(refute_0_7,plain,
    colinear(X_270,X_270,X_271),
    inference(resolve,[$cnf( between(X_270,X_270,X_271) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    colinear(x,x,y),
    inference(subst,[],[refute_0_7:[bind(X_270,$fot(x)),bind(X_271,$fot(y))]]) ).

cnf(refute_0_9,plain,
    ( ~ colinear(x,y,x)
    | x = y ),
    inference(resolve,[$cnf( colinear(x,x,y) )],[refute_0_8,refute_0_4]) ).

cnf(refute_0_10,plain,
    between(X_304,X_303,X_303),
    inference(subst,[],[t3:[bind(U,$fot(X_304)),bind(V,$fot(X_303))]]) ).

cnf(refute_0_11,plain,
    ( ~ between(X_304,X_303,X_303)
    | colinear(X_303,X_304,X_303) ),
    inference(subst,[],[colinearity2:[bind(X,$fot(X_303)),bind(Y,$fot(X_304)),bind(Z,$fot(X_303))]]) ).

cnf(refute_0_12,plain,
    colinear(X_303,X_304,X_303),
    inference(resolve,[$cnf( between(X_304,X_303,X_303) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    colinear(x,y,x),
    inference(subst,[],[refute_0_12:[bind(X_303,$fot(x)),bind(X_304,$fot(y))]]) ).

cnf(refute_0_14,plain,
    x = y,
    inference(resolve,[$cnf( colinear(x,y,x) )],[refute_0_13,refute_0_9]) ).

cnf(refute_0_15,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_16,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_17,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( x != y
    | y = x ),
    inference(subst,[],[refute_0_17:[bind(X0,$fot(x)),bind(Y0,$fot(y))]]) ).

cnf(refute_0_19,plain,
    y = x,
    inference(resolve,[$cnf( $equal(x,y) )],[refute_0_14,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( y != x
    | ~ colinear(x,x,x)
    | colinear(x,x,y) ),
    introduced(tautology,[equality,[$cnf( ~ colinear(x,x,y) ),[2],$fot(x)]]) ).

cnf(refute_0_21,plain,
    ( ~ colinear(x,x,x)
    | colinear(x,x,y) ),
    inference(resolve,[$cnf( $equal(y,x) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( ~ colinear(x,x,x)
    | ~ colinear(x,y,x)
    | ~ colinear(x,z,y)
    | ~ colinear(y,x,x) ),
    inference(resolve,[$cnf( colinear(x,x,y) )],[refute_0_21,part_2]) ).

cnf(refute_0_23,plain,
    ( y != x
    | ~ colinear(x,x,x)
    | colinear(x,y,x) ),
    introduced(tautology,[equality,[$cnf( ~ colinear(x,y,x) ),[1],$fot(x)]]) ).

cnf(refute_0_24,plain,
    ( ~ colinear(x,x,x)
    | colinear(x,y,x) ),
    inference(resolve,[$cnf( $equal(y,x) )],[refute_0_19,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( ~ colinear(x,x,x)
    | ~ colinear(x,z,y)
    | ~ colinear(y,x,x) ),
    inference(resolve,[$cnf( colinear(x,y,x) )],[refute_0_24,refute_0_22]) ).

cnf(refute_0_26,plain,
    ( y != x
    | ~ colinear(x,z,x)
    | colinear(x,z,y) ),
    introduced(tautology,[equality,[$cnf( ~ colinear(x,z,y) ),[2],$fot(x)]]) ).

cnf(refute_0_27,plain,
    ( ~ colinear(x,z,x)
    | colinear(x,z,y) ),
    inference(resolve,[$cnf( $equal(y,x) )],[refute_0_19,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( ~ colinear(x,x,x)
    | ~ colinear(x,z,x)
    | ~ colinear(y,x,x) ),
    inference(resolve,[$cnf( colinear(x,z,y) )],[refute_0_27,refute_0_25]) ).

cnf(refute_0_29,plain,
    ( y != x
    | ~ colinear(x,x,x)
    | colinear(y,x,x) ),
    introduced(tautology,[equality,[$cnf( ~ colinear(y,x,x) ),[0],$fot(x)]]) ).

cnf(refute_0_30,plain,
    ( ~ colinear(x,x,x)
    | colinear(y,x,x) ),
    inference(resolve,[$cnf( $equal(y,x) )],[refute_0_19,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( ~ colinear(x,x,x)
    | ~ colinear(x,z,x) ),
    inference(resolve,[$cnf( colinear(y,x,x) )],[refute_0_30,refute_0_28]) ).

cnf(refute_0_32,plain,
    colinear(x,x,x),
    inference(subst,[],[refute_0_12:[bind(X_303,$fot(x)),bind(X_304,$fot(x))]]) ).

cnf(refute_0_33,plain,
    ~ colinear(x,z,x),
    inference(resolve,[$cnf( colinear(x,x,x) )],[refute_0_32,refute_0_31]) ).

cnf(refute_0_34,plain,
    colinear(x,z,x),
    inference(subst,[],[refute_0_12:[bind(X_303,$fot(x)),bind(X_304,$fot(z))]]) ).

cnf(refute_0_35,plain,
    $false,
    inference(resolve,[$cnf( colinear(x,z,x) )],[refute_0_34,refute_0_33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO067-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n024.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 07:42:47 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.56  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.56  
% 0.18/0.56  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.56  
%------------------------------------------------------------------------------