TSTP Solution File: GEO058-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO058-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 05:23:57 EDT 2022
% Result : Unsatisfiable 3.63s 3.80s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 18 unt; 0 nHn; 24 RR)
% Number of literals : 53 ( 21 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 48 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) ) ).
cnf(identity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,Z)
| X = Y ) ).
cnf(segment_construction2,axiom,
equidistant(Y,extension(X,Y,W,V),W,V) ).
cnf(reflection,axiom,
reflection(U,V) = extension(U,V,U,V) ).
cnf(v_equals_reflection,hypothesis,
v = reflection(u,v) ).
cnf(prove_u_equals_v,negated_conjecture,
u != v ).
cnf(refute_0_0,plain,
( ~ equidistant(u,v,v,v)
| u = v ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(v))]]) ).
cnf(refute_0_1,plain,
equidistant(X_31,extension(X,X_31,X_33,X_30),X_33,X_30),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_30)),bind(W,$fot(X_33)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_2,plain,
( ~ equidistant(X_31,extension(X,X_31,X_33,X_30),X_33,X_30)
| equidistant(X_33,X_30,X_33,X_30) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_30)),bind(V2,$fot(X_33)),bind(W,$fot(X_30)),bind(X,$fot(X_31)),bind(Y,$fot(extension(X,X_31,X_33,X_30))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_3,plain,
equidistant(X_33,X_30,X_33,X_30),
inference(resolve,[$cnf( equidistant(X_31,extension(X,X_31,X_33,X_30),X_33,X_30) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
equidistant(v,v,v,v),
inference(subst,[],[refute_0_3:[bind(X_30,$fot(v)),bind(X_33,$fot(v))]]) ).
cnf(refute_0_5,plain,
equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_12)),bind(W,$fot(X_13)),bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_6,plain,
reflection(X_13,X_12) = extension(X_13,X_12,X_13,X_12),
inference(subst,[],[reflection:[bind(U,$fot(X_13)),bind(V,$fot(X_12))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( reflection(X_13,X_12) != extension(X_13,X_12,X_13,X_12)
| extension(X_13,X_12,X_13,X_12) = reflection(X_13,X_12) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(reflection(X_13,X_12))),bind(Y0,$fot(extension(X_13,X_12,X_13,X_12)))]]) ).
cnf(refute_0_11,plain,
extension(X_13,X_12,X_13,X_12) = reflection(X_13,X_12),
inference(resolve,[$cnf( $equal(reflection(X_13,X_12),extension(X_13,X_12,X_13,X_12)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( extension(X_13,X_12,X_13,X_12) != reflection(X_13,X_12)
| ~ equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12)
| equidistant(X_12,reflection(X_13,X_12),X_13,X_12) ),
introduced(tautology,[equality,[$cnf( equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12) ),[1],$fot(reflection(X_13,X_12))]]) ).
cnf(refute_0_13,plain,
( ~ equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12)
| equidistant(X_12,reflection(X_13,X_12),X_13,X_12) ),
inference(resolve,[$cnf( $equal(extension(X_13,X_12,X_13,X_12),reflection(X_13,X_12)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
equidistant(X_12,reflection(X_13,X_12),X_13,X_12),
inference(resolve,[$cnf( equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
equidistant(v,reflection(u,v),u,v),
inference(subst,[],[refute_0_14:[bind(X_12,$fot(v)),bind(X_13,$fot(u))]]) ).
cnf(refute_0_16,plain,
( v != reflection(u,v)
| reflection(u,v) = v ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(v)),bind(Y0,$fot(reflection(u,v)))]]) ).
cnf(refute_0_17,plain,
reflection(u,v) = v,
inference(resolve,[$cnf( $equal(v,reflection(u,v)) )],[v_equals_reflection,refute_0_16]) ).
cnf(refute_0_18,plain,
( reflection(u,v) != v
| ~ equidistant(v,reflection(u,v),u,v)
| equidistant(v,v,u,v) ),
introduced(tautology,[equality,[$cnf( equidistant(v,reflection(u,v),u,v) ),[1],$fot(v)]]) ).
cnf(refute_0_19,plain,
( ~ equidistant(v,reflection(u,v),u,v)
| equidistant(v,v,u,v) ),
inference(resolve,[$cnf( $equal(reflection(u,v),v) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
equidistant(v,v,u,v),
inference(resolve,[$cnf( equidistant(v,reflection(u,v),u,v) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ equidistant(v,v,X_413,X_414)
| ~ equidistant(v,v,u,v)
| equidistant(u,v,X_413,X_414) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(v)),bind(V2,$fot(X_413)),bind(W,$fot(X_414)),bind(X,$fot(v)),bind(Y,$fot(v)),bind(Z,$fot(u))]]) ).
cnf(refute_0_22,plain,
( ~ equidistant(v,v,X_413,X_414)
| equidistant(u,v,X_413,X_414) ),
inference(resolve,[$cnf( equidistant(v,v,u,v) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ equidistant(v,v,v,v)
| equidistant(u,v,v,v) ),
inference(subst,[],[refute_0_22:[bind(X_413,$fot(v)),bind(X_414,$fot(v))]]) ).
cnf(refute_0_24,plain,
equidistant(u,v,v,v),
inference(resolve,[$cnf( equidistant(v,v,v,v) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
u = v,
inference(resolve,[$cnf( equidistant(u,v,v,v) )],[refute_0_24,refute_0_0]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(u,v) )],[refute_0_25,prove_u_equals_v]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO058-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 15:02:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.63/3.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.63/3.80
% 3.63/3.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.63/3.80
%------------------------------------------------------------------------------