TSTP Solution File: GEO002-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO002-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 05:23:25 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 19 unt; 0 nHn; 20 RR)
% Number of literals : 58 ( 22 equ; 23 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 : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 85 ( 10 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(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b) ).
cnf(refute_0_0,plain,
( ~ between(Y,Z,Z)
| between(Z,Z,outer_pasch(Z,Y,Y,Z,Z)) ),
inference(subst,[],[outer_pasch2:[bind(V,$fot(Z)),bind(W,$fot(Z)),bind(X,$fot(Y))]]) ).
cnf(refute_0_1,plain,
( ~ between(X_28,outer_pasch(X_29,X_28,X_28,X_29,X_29),X_28)
| X_28 = outer_pasch(X_29,X_28,X_28,X_29,X_29) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(X_28)),bind(Y,$fot(outer_pasch(X_29,X_28,X_28,X_29,X_29)))]]) ).
cnf(refute_0_2,plain,
( ~ between(Y,Z,Z)
| between(Y,outer_pasch(Z,Y,Y,Z,Z),Y) ),
inference(subst,[],[outer_pasch1:[bind(V,$fot(Z)),bind(W,$fot(Z)),bind(X,$fot(Y))]]) ).
cnf(refute_0_3,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_4,plain,
equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_14)),bind(W,$fot(X_14)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_5,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,$fot(X_14))]]) ).
cnf(refute_0_6,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_6:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_8,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_9,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_12,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_14,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_3,refute_0_14]) ).
cnf(refute_0_16,plain,
between(Y,Z,Z),
inference(subst,[],[refute_0_15:[bind(X,$fot(Y)),bind(Y,$fot(Z))]]) ).
cnf(refute_0_17,plain,
between(Y,outer_pasch(Z,Y,Y,Z,Z),Y),
inference(resolve,[$cnf( between(Y,Z,Z) )],[refute_0_16,refute_0_2]) ).
cnf(refute_0_18,plain,
between(X_28,outer_pasch(X_29,X_28,X_28,X_29,X_29),X_28),
inference(subst,[],[refute_0_17:[bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_19,plain,
X_28 = outer_pasch(X_29,X_28,X_28,X_29,X_29),
inference(resolve,[$cnf( between(X_28,outer_pasch(X_29,X_28,X_28,X_29,X_29),X_28) )],[refute_0_18,refute_0_1]) ).
cnf(refute_0_20,plain,
( X_28 != outer_pasch(X_29,X_28,X_28,X_29,X_29)
| outer_pasch(X_29,X_28,X_28,X_29,X_29) = X_28 ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(X_28)),bind(Y0,$fot(outer_pasch(X_29,X_28,X_28,X_29,X_29)))]]) ).
cnf(refute_0_21,plain,
outer_pasch(X_29,X_28,X_28,X_29,X_29) = X_28,
inference(resolve,[$cnf( $equal(X_28,outer_pasch(X_29,X_28,X_28,X_29,X_29)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
outer_pasch(Z,Y,Y,Z,Z) = Y,
inference(subst,[],[refute_0_21:[bind(X_28,$fot(Y)),bind(X_29,$fot(Z))]]) ).
cnf(refute_0_23,plain,
( outer_pasch(Z,Y,Y,Z,Z) != Y
| ~ between(Z,Z,outer_pasch(Z,Y,Y,Z,Z))
| between(Z,Z,Y) ),
introduced(tautology,[equality,[$cnf( between(Z,Z,outer_pasch(Z,Y,Y,Z,Z)) ),[2],$fot(Y)]]) ).
cnf(refute_0_24,plain,
( ~ between(Z,Z,outer_pasch(Z,Y,Y,Z,Z))
| between(Z,Z,Y) ),
inference(resolve,[$cnf( $equal(outer_pasch(Z,Y,Y,Z,Z),Y) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ between(Y,Z,Z)
| between(Z,Z,Y) ),
inference(resolve,[$cnf( between(Z,Z,outer_pasch(Z,Y,Y,Z,Z)) )],[refute_0_0,refute_0_24]) ).
cnf(refute_0_26,plain,
between(Z,Z,Y),
inference(resolve,[$cnf( between(Y,Z,Z) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
between(a,a,b),
inference(subst,[],[refute_0_26:[bind(Y,$fot(b)),bind(Z,$fot(a))]]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( between(a,a,b) )],[refute_0_27,prove_a_between_a_and_b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO002-1 : TPTP v8.1.0. Bugfixed v2.5.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 14:03:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------