%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO001-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 05:23:24 EDT 2022
% Result : Unsatisfiable 30.73s 30.98s
% Output : CNFRefutation 30.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 21 unt; 0 nHn; 28 RR)
% Number of literals : 68 ( 21 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 71 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_betweeness,axiom,
( ~ between(X,Y,X)
| X = Y ) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,Z)
| X = Y ) ).
cnf(outer_pasch1,axiom,
( ~ between(X,W,V)
| ~ between(Y,V,Z)
| between(X,outer_pasch(W,X,Y,Z,V),Y) ) ).
cnf(outer_pasch2,axiom,
( ~ between(X,W,V)
| ~ between(Y,V,Z)
| between(Z,W,outer_pasch(W,X,Y,Z,V)) ) ).
cnf(segment_construction1,axiom,
between(X,Y,extension(X,Y,W,V)) ).
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V) ).
cnf(b_between_a_and_c,hypothesis,
between(a,b,c) ).
cnf(prove_b_between_c_and_a,negated_conjecture,
~ between(c,b,a) ).
cnf(refute_0_0,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_1,plain,
equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_14)),bind(W,$fot(X_14)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_2,plain,
( ~ equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14)
| X_12 = extension(X,X_12,X_14,X_14) ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_12)),bind(Y,$fot(extension(X,X_12,X_14,X_14))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_3,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_3:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_9,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_11,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
between(X_4394,c,c),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_4394)),bind(Y,$fot(c))]]) ).
cnf(refute_0_14,plain,
( ~ between(X_4392,c,X_4393)
| ~ between(a,b,c)
| between(X_4393,b,outer_pasch(b,a,X_4392,X_4393,c)) ),
inference(subst,[],[outer_pasch2:[bind(V,$fot(c)),bind(W,$fot(b)),bind(X,$fot(a)),bind(Y,$fot(X_4392)),bind(Z,$fot(X_4393))]]) ).
cnf(refute_0_15,plain,
( ~ between(X_4392,c,X_4393)
| between(X_4393,b,outer_pasch(b,a,X_4392,X_4393,c)) ),
inference(resolve,[$cnf( between(a,b,c) )],[b_between_a_and_c,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ between(X_4394,c,c)
| between(c,b,outer_pasch(b,a,X_4394,c,c)) ),
inference(subst,[],[refute_0_15:[bind(X_4392,$fot(X_4394)),bind(X_4393,$fot(c))]]) ).
cnf(refute_0_17,plain,
between(c,b,outer_pasch(b,a,X_4394,c,c)),
inference(resolve,[$cnf( between(X_4394,c,c) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
between(c,b,outer_pasch(b,a,a,c,c)),
inference(subst,[],[refute_0_17:[bind(X_4394,$fot(a))]]) ).
cnf(refute_0_19,plain,
( ~ between(a,outer_pasch(b,a,a,c,c),a)
| a = outer_pasch(b,a,a,c,c) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(a)),bind(Y,$fot(outer_pasch(b,a,a,c,c)))]]) ).
cnf(refute_0_20,plain,
between(X_91,c,c),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_91)),bind(Y,$fot(c))]]) ).
cnf(refute_0_21,plain,
( ~ between(X_89,c,X_90)
| ~ between(a,b,c)
| between(a,outer_pasch(b,a,X_89,X_90,c),X_89) ),
inference(subst,[],[outer_pasch1:[bind(V,$fot(c)),bind(W,$fot(b)),bind(X,$fot(a)),bind(Y,$fot(X_89)),bind(Z,$fot(X_90))]]) ).
cnf(refute_0_22,plain,
( ~ between(X_89,c,X_90)
| between(a,outer_pasch(b,a,X_89,X_90,c),X_89) ),
inference(resolve,[$cnf( between(a,b,c) )],[b_between_a_and_c,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ between(X_91,c,c)
| between(a,outer_pasch(b,a,X_91,c,c),X_91) ),
inference(subst,[],[refute_0_22:[bind(X_89,$fot(X_91)),bind(X_90,$fot(c))]]) ).
cnf(refute_0_24,plain,
between(a,outer_pasch(b,a,X_91,c,c),X_91),
inference(resolve,[$cnf( between(X_91,c,c) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
between(a,outer_pasch(b,a,a,c,c),a),
inference(subst,[],[refute_0_24:[bind(X_91,$fot(a))]]) ).
cnf(refute_0_26,plain,
a = outer_pasch(b,a,a,c,c),
inference(resolve,[$cnf( between(a,outer_pasch(b,a,a,c,c),a) )],[refute_0_25,refute_0_19]) ).
cnf(refute_0_27,plain,
( a != outer_pasch(b,a,a,c,c)
| outer_pasch(b,a,a,c,c) = a ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(a)),bind(Y0,$fot(outer_pasch(b,a,a,c,c)))]]) ).
cnf(refute_0_28,plain,
outer_pasch(b,a,a,c,c) = a,
inference(resolve,[$cnf( $equal(a,outer_pasch(b,a,a,c,c)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( outer_pasch(b,a,a,c,c) != a
| ~ between(c,b,outer_pasch(b,a,a,c,c))
| between(c,b,a) ),
introduced(tautology,[equality,[$cnf( between(c,b,outer_pasch(b,a,a,c,c)) ),[2],$fot(a)]]) ).
cnf(refute_0_30,plain,
( ~ between(c,b,outer_pasch(b,a,a,c,c))
| between(c,b,a) ),
inference(resolve,[$cnf( $equal(outer_pasch(b,a,a,c,c),a) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
between(c,b,a),
inference(resolve,[$cnf( between(c,b,outer_pasch(b,a,a,c,c)) )],[refute_0_18,refute_0_30]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( between(c,b,a) )],[refute_0_31,prove_b_between_c_and_a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO001-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 13:12:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.73/30.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.73/30.98
% 30.73/30.98 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.73/30.98
%------------------------------------------------------------------------------