TSTP Solution File: GEO064-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO064-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 4.78s 4.96s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 22 unt; 0 nHn; 31 RR)
% Number of literals : 73 ( 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 : 74 ( 11 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(colinearity1,axiom,
( ~ between(X,Y,Z)
| colinear(X,Y,Z) ) ).
cnf(v_between_w_and_u,hypothesis,
between(w,v,u) ).
cnf(prove_uvw_colinear,negated_conjecture,
~ colinear(u,v,w) ).
cnf(refute_0_0,plain,
( ~ between(u,v,w)
| colinear(u,v,w) ),
inference(subst,[],[colinearity1:[bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(w))]]) ).
cnf(refute_0_1,plain,
between(X,Y,extension(X,Y,V,V)),
inference(subst,[],[segment_construction1:[bind(W,$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_442,u,u),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_442)),bind(Y,$fot(u))]]) ).
cnf(refute_0_15,plain,
( ~ between(X_404,X_403,u)
| ~ between(w,v,u)
| between(X_403,inner_pasch(w,v,u,X_403,X_404),w) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(w)),bind(V,$fot(v)),bind(W,$fot(u)),bind(X,$fot(X_403)),bind(Y,$fot(X_404))]]) ).
cnf(refute_0_16,plain,
( ~ between(X_404,X_403,u)
| between(X_403,inner_pasch(w,v,u,X_403,X_404),w) ),
inference(resolve,[$cnf( between(w,v,u) )],[v_between_w_and_u,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ between(X_442,u,u)
| between(u,inner_pasch(w,v,u,u,X_442),w) ),
inference(subst,[],[refute_0_16:[bind(X_403,$fot(u)),bind(X_404,$fot(X_442))]]) ).
cnf(refute_0_18,plain,
between(u,inner_pasch(w,v,u,u,X_442),w),
inference(resolve,[$cnf( between(X_442,u,u) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
between(u,inner_pasch(w,v,u,u,v),w),
inference(subst,[],[refute_0_18:[bind(X_442,$fot(v))]]) ).
cnf(refute_0_20,plain,
( ~ between(v,inner_pasch(w,v,u,u,v),v)
| v = inner_pasch(w,v,u,u,v) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(v)),bind(Y,$fot(inner_pasch(w,v,u,u,v)))]]) ).
cnf(refute_0_21,plain,
between(X_206,u,u),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_206)),bind(Y,$fot(u))]]) ).
cnf(refute_0_22,plain,
( ~ between(X_204,X_203,u)
| ~ between(w,v,u)
| between(v,inner_pasch(w,v,u,X_203,X_204),X_204) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(w)),bind(V,$fot(v)),bind(W,$fot(u)),bind(X,$fot(X_203)),bind(Y,$fot(X_204))]]) ).
cnf(refute_0_23,plain,
( ~ between(X_204,X_203,u)
| between(v,inner_pasch(w,v,u,X_203,X_204),X_204) ),
inference(resolve,[$cnf( between(w,v,u) )],[v_between_w_and_u,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ between(X_206,u,u)
| between(v,inner_pasch(w,v,u,u,X_206),X_206) ),
inference(subst,[],[refute_0_23:[bind(X_203,$fot(u)),bind(X_204,$fot(X_206))]]) ).
cnf(refute_0_25,plain,
between(v,inner_pasch(w,v,u,u,X_206),X_206),
inference(resolve,[$cnf( between(X_206,u,u) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
between(v,inner_pasch(w,v,u,u,v),v),
inference(subst,[],[refute_0_25:[bind(X_206,$fot(v))]]) ).
cnf(refute_0_27,plain,
v = inner_pasch(w,v,u,u,v),
inference(resolve,[$cnf( between(v,inner_pasch(w,v,u,u,v),v) )],[refute_0_26,refute_0_20]) ).
cnf(refute_0_28,plain,
( v != inner_pasch(w,v,u,u,v)
| inner_pasch(w,v,u,u,v) = v ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(v)),bind(Y0,$fot(inner_pasch(w,v,u,u,v)))]]) ).
cnf(refute_0_29,plain,
inner_pasch(w,v,u,u,v) = v,
inference(resolve,[$cnf( $equal(v,inner_pasch(w,v,u,u,v)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( inner_pasch(w,v,u,u,v) != v
| ~ between(u,inner_pasch(w,v,u,u,v),w)
| between(u,v,w) ),
introduced(tautology,[equality,[$cnf( between(u,inner_pasch(w,v,u,u,v),w) ),[1],$fot(v)]]) ).
cnf(refute_0_31,plain,
( ~ between(u,inner_pasch(w,v,u,u,v),w)
| between(u,v,w) ),
inference(resolve,[$cnf( $equal(inner_pasch(w,v,u,u,v),v) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
between(u,v,w),
inference(resolve,[$cnf( between(u,inner_pasch(w,v,u,u,v),w) )],[refute_0_19,refute_0_31]) ).
cnf(refute_0_33,plain,
colinear(u,v,w),
inference(resolve,[$cnf( between(u,v,w) )],[refute_0_32,refute_0_0]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( colinear(u,v,w) )],[refute_0_33,prove_uvw_colinear]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO064-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sat Jun 18 00:50:16 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.10/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.78/4.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.78/4.96
% 4.78/4.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.78/4.96
%------------------------------------------------------------------------------