TSTP Solution File: GEO039-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO039-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 05:23:47 EDT 2022
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 37 ( 20 unt; 0 nHn; 28 RR)
% Number of literals : 59 ( 27 equ; 25 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; 4 con; 0-4 aty)
% Number of variables : 47 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,Z)
| X = Y ) ).
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(identity_for_betweeness,axiom,
( ~ between(X,Y,X)
| X = Y ) ).
cnf(w_between_u_and_x,hypothesis,
between(u,w,x) ).
cnf(u_is_x,hypothesis,
u = x ).
cnf(prove_corollary,negated_conjecture,
~ between(v,w,x) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( u != x
| x = u ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(u)),bind(Y0,$fot(x))]]) ).
cnf(refute_0_4,plain,
x = u,
inference(resolve,[$cnf( $equal(u,x) )],[u_is_x,refute_0_3]) ).
cnf(refute_0_5,plain,
( x != u
| ~ between(v,w,u)
| between(v,w,x) ),
introduced(tautology,[equality,[$cnf( ~ between(v,w,x) ),[2],$fot(u)]]) ).
cnf(refute_0_6,plain,
( ~ between(v,w,u)
| between(v,w,x) ),
inference(resolve,[$cnf( $equal(x,u) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
~ between(v,w,u),
inference(resolve,[$cnf( between(v,w,x) )],[refute_0_6,prove_corollary]) ).
cnf(refute_0_8,plain,
( x != u
| ~ between(u,w,x)
| between(u,w,u) ),
introduced(tautology,[equality,[$cnf( between(u,w,x) ),[2],$fot(u)]]) ).
cnf(refute_0_9,plain,
( ~ between(u,w,x)
| between(u,w,u) ),
inference(resolve,[$cnf( $equal(x,u) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
between(u,w,u),
inference(resolve,[$cnf( between(u,w,x) )],[w_between_u_and_x,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ between(u,w,u)
| u = w ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(u)),bind(Y,$fot(w))]]) ).
cnf(refute_0_12,plain,
u = w,
inference(resolve,[$cnf( between(u,w,u) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( u != w
| w = u ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(u)),bind(Y0,$fot(w))]]) ).
cnf(refute_0_14,plain,
w = u,
inference(resolve,[$cnf( $equal(u,w) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( w != u
| ~ between(v,u,u)
| between(v,w,u) ),
introduced(tautology,[equality,[$cnf( ~ between(v,w,u) ),[1],$fot(u)]]) ).
cnf(refute_0_16,plain,
( ~ between(v,u,u)
| between(v,w,u) ),
inference(resolve,[$cnf( $equal(w,u) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
~ between(v,u,u),
inference(resolve,[$cnf( between(v,w,u) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_19,plain,
equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_14)),bind(W,$fot(X_14)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_20,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,$fot(X_14))]]) ).
cnf(refute_0_21,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_21:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_23,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_24,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_26,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_18,refute_0_26]) ).
cnf(refute_0_28,plain,
between(v,u,u),
inference(subst,[],[refute_0_27:[bind(X,$fot(v)),bind(Y,$fot(u))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( between(v,u,u) )],[refute_0_28,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : GEO039-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sat Jun 18 05:31:08 EDT 2022
% 0.15/0.38 % CPUTime :
% 0.15/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41
% 0.15/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.15/0.41
%------------------------------------------------------------------------------