%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO065-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 05:24:00 EDT 2022
% Result : Unsatisfiable 1.45s 1.61s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 45 ( 23 unt; 0 nHn; 30 RR)
% Number of literals : 74 ( 21 equ; 30 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 77 ( 13 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(inner_pasch1,axiom,
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) ).
cnf(inner_pasch2,axiom,
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) ).
cnf(colinearity2,axiom,
( ~ between(Y,Z,X)
| colinear(X,Y,Z) ) ).
cnf(w_between_u_and_v,hypothesis,
between(u,w,v) ).
cnf(prove_uvw_colinear,negated_conjecture,
~ colinear(u,v,w) ).
cnf(refute_0_0,plain,
( ~ between(v,inner_pasch(X_223,v,v,w,u),u)
| colinear(u,v,inner_pasch(X_223,v,v,w,u)) ),
inference(subst,[],[colinearity2:[bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(inner_pasch(X_223,v,v,w,u)))]]) ).
cnf(refute_0_1,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$fot(V))]]) ).
cnf(refute_0_2,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,$fot(X_12))]]) ).
cnf(refute_0_3,plain,
( ~ equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14)
| X_12 = extension(X,X_12,X_14,X_14) ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_12)),bind(Y,$fot(extension(X,X_12,X_14,X_14))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_4,plain,
X_12 = extension(X,X_12,X_14,X_14),
inference(resolve,[$cnf( equidistant(X_12,extension(X,X_12,X_14,X_14),X_14,X_14) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
Y = extension(X,Y,V,V),
inference(subst,[],[refute_0_4:[bind(X_12,$fot(Y)),bind(X_14,$fot(V))]]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( Y != extension(X,Y,V,V)
| extension(X,Y,V,V) = Y ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(Y)),bind(Y0,$fot(extension(X,Y,V,V)))]]) ).
cnf(refute_0_10,plain,
extension(X,Y,V,V) = Y,
inference(resolve,[$cnf( $equal(Y,extension(X,Y,V,V)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( extension(X,Y,V,V) != Y
| ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
introduced(tautology,[equality,[$cnf( between(X,Y,extension(X,Y,V,V)) ),[2],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( ~ between(X,Y,extension(X,Y,V,V))
| between(X,Y,Y) ),
inference(resolve,[$cnf( $equal(extension(X,Y,V,V),Y) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
between(X,Y,Y),
inference(resolve,[$cnf( between(X,Y,extension(X,Y,V,V)) )],[refute_0_1,refute_0_12]) ).
cnf(refute_0_14,plain,
between(X_221,v,v),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_221)),bind(Y,$fot(v))]]) ).
cnf(refute_0_15,plain,
( ~ between(X_192,X_193,v)
| ~ between(u,w,v)
| between(X_193,inner_pasch(X_192,X_193,v,w,u),u) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(X_192)),bind(V,$fot(X_193)),bind(W,$fot(v)),bind(X,$fot(w)),bind(Y,$fot(u))]]) ).
cnf(refute_0_16,plain,
( ~ between(X_192,X_193,v)
| between(X_193,inner_pasch(X_192,X_193,v,w,u),u) ),
inference(resolve,[$cnf( between(u,w,v) )],[w_between_u_and_v,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ between(X_221,v,v)
| between(v,inner_pasch(X_221,v,v,w,u),u) ),
inference(subst,[],[refute_0_16:[bind(X_192,$fot(X_221)),bind(X_193,$fot(v))]]) ).
cnf(refute_0_18,plain,
between(v,inner_pasch(X_221,v,v,w,u),u),
inference(resolve,[$cnf( between(X_221,v,v) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
between(v,inner_pasch(X_223,v,v,w,u),u),
inference(subst,[],[refute_0_18:[bind(X_221,$fot(X_223))]]) ).
cnf(refute_0_20,plain,
colinear(u,v,inner_pasch(X_223,v,v,w,u)),
inference(resolve,[$cnf( between(v,inner_pasch(X_223,v,v,w,u),u) )],[refute_0_19,refute_0_0]) ).
cnf(refute_0_21,plain,
colinear(u,v,inner_pasch(w,v,v,w,u)),
inference(subst,[],[refute_0_20:[bind(X_223,$fot(w))]]) ).
cnf(refute_0_22,plain,
( ~ between(w,inner_pasch(w,v,v,w,u),w)
| w = inner_pasch(w,v,v,w,u) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(w)),bind(Y,$fot(inner_pasch(w,v,v,w,u)))]]) ).
cnf(refute_0_23,plain,
between(X_315,v,v),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_315)),bind(Y,$fot(v))]]) ).
cnf(refute_0_24,plain,
( ~ between(X_310,X_311,v)
| ~ between(u,w,v)
| between(w,inner_pasch(X_310,X_311,v,w,u),X_310) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(X_310)),bind(V,$fot(X_311)),bind(W,$fot(v)),bind(X,$fot(w)),bind(Y,$fot(u))]]) ).
cnf(refute_0_25,plain,
( ~ between(X_310,X_311,v)
| between(w,inner_pasch(X_310,X_311,v,w,u),X_310) ),
inference(resolve,[$cnf( between(u,w,v) )],[w_between_u_and_v,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ between(X_315,v,v)
| between(w,inner_pasch(X_315,v,v,w,u),X_315) ),
inference(subst,[],[refute_0_25:[bind(X_310,$fot(X_315)),bind(X_311,$fot(v))]]) ).
cnf(refute_0_27,plain,
between(w,inner_pasch(X_315,v,v,w,u),X_315),
inference(resolve,[$cnf( between(X_315,v,v) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
between(w,inner_pasch(w,v,v,w,u),w),
inference(subst,[],[refute_0_27:[bind(X_315,$fot(w))]]) ).
cnf(refute_0_29,plain,
w = inner_pasch(w,v,v,w,u),
inference(resolve,[$cnf( between(w,inner_pasch(w,v,v,w,u),w) )],[refute_0_28,refute_0_22]) ).
cnf(refute_0_30,plain,
( w != inner_pasch(w,v,v,w,u)
| inner_pasch(w,v,v,w,u) = w ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(w)),bind(Y0,$fot(inner_pasch(w,v,v,w,u)))]]) ).
cnf(refute_0_31,plain,
inner_pasch(w,v,v,w,u) = w,
inference(resolve,[$cnf( $equal(w,inner_pasch(w,v,v,w,u)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( inner_pasch(w,v,v,w,u) != w
| ~ colinear(u,v,inner_pasch(w,v,v,w,u))
| colinear(u,v,w) ),
introduced(tautology,[equality,[$cnf( colinear(u,v,inner_pasch(w,v,v,w,u)) ),[2],$fot(w)]]) ).
cnf(refute_0_33,plain,
( ~ colinear(u,v,inner_pasch(w,v,v,w,u))
| colinear(u,v,w) ),
inference(resolve,[$cnf( $equal(inner_pasch(w,v,v,w,u),w) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
colinear(u,v,w),
inference(resolve,[$cnf( colinear(u,v,inner_pasch(w,v,v,w,u)) )],[refute_0_21,refute_0_33]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( colinear(u,v,w) )],[refute_0_34,prove_uvw_colinear]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO065-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 22:26:58 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.45/1.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.45/1.61
% 1.45/1.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.45/1.61
%------------------------------------------------------------------------------