TSTP Solution File: GEO056-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO056-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 05:23:55 EDT 2022
% Result : Unsatisfiable 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 38 ( 20 unt; 0 nHn; 28 RR)
% Number of literals : 62 ( 51 equ; 27 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 : 33 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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(u_equals_v,hypothesis,
u = v ).
cnf(prove_v_equals_reflection,negated_conjecture,
v != reflection(u,v) ).
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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( u != v
| v = u ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(u)),bind(Y0,$fot(v))]]) ).
cnf(refute_0_4,plain,
v = u,
inference(resolve,[$cnf( $equal(u,v) )],[u_equals_v,refute_0_3]) ).
cnf(refute_0_5,plain,
( u != reflection(u,v)
| v != u
| v = reflection(u,v) ),
introduced(tautology,[equality,[$cnf( $equal(v,u) ),[1],$fot(reflection(u,v))]]) ).
cnf(refute_0_6,plain,
( u != reflection(u,v)
| v = reflection(u,v) ),
inference(resolve,[$cnf( $equal(v,u) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
reflection(u,v) = reflection(u,v),
introduced(tautology,[refl,[$fot(reflection(u,v))]]) ).
cnf(refute_0_8,plain,
( reflection(u,v) != reflection(u,v)
| v != u
| reflection(u,v) = reflection(u,u) ),
introduced(tautology,[equality,[$cnf( $equal(reflection(u,v),reflection(u,v)) ),[1,1],$fot(u)]]) ).
cnf(refute_0_9,plain,
( v != u
| reflection(u,v) = reflection(u,u) ),
inference(resolve,[$cnf( $equal(reflection(u,v),reflection(u,v)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
reflection(u,v) = reflection(u,u),
inference(resolve,[$cnf( $equal(v,u) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( reflection(u,v) != reflection(u,u)
| u != reflection(u,u)
| u = reflection(u,v) ),
introduced(tautology,[equality,[$cnf( ~ $equal(u,reflection(u,v)) ),[1],$fot(reflection(u,u))]]) ).
cnf(refute_0_12,plain,
( u != reflection(u,u)
| u = reflection(u,v) ),
inference(resolve,[$cnf( $equal(reflection(u,v),reflection(u,u)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( u != reflection(u,u)
| v = reflection(u,v) ),
inference(resolve,[$cnf( $equal(u,reflection(u,v)) )],[refute_0_12,refute_0_6]) ).
cnf(refute_0_14,plain,
u != reflection(u,u),
inference(resolve,[$cnf( $equal(v,reflection(u,v)) )],[refute_0_13,prove_v_equals_reflection]) ).
cnf(refute_0_15,plain,
equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_12)),bind(W,$fot(X_13)),bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
reflection(X_13,X_12) = extension(X_13,X_12,X_13,X_12),
inference(subst,[],[reflection:[bind(U,$fot(X_13)),bind(V,$fot(X_12))]]) ).
cnf(refute_0_17,plain,
( reflection(X_13,X_12) != extension(X_13,X_12,X_13,X_12)
| extension(X_13,X_12,X_13,X_12) = reflection(X_13,X_12) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(reflection(X_13,X_12))),bind(Y0,$fot(extension(X_13,X_12,X_13,X_12)))]]) ).
cnf(refute_0_18,plain,
extension(X_13,X_12,X_13,X_12) = reflection(X_13,X_12),
inference(resolve,[$cnf( $equal(reflection(X_13,X_12),extension(X_13,X_12,X_13,X_12)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( extension(X_13,X_12,X_13,X_12) != reflection(X_13,X_12)
| ~ equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12)
| equidistant(X_12,reflection(X_13,X_12),X_13,X_12) ),
introduced(tautology,[equality,[$cnf( equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12) ),[1],$fot(reflection(X_13,X_12))]]) ).
cnf(refute_0_20,plain,
( ~ equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12)
| equidistant(X_12,reflection(X_13,X_12),X_13,X_12) ),
inference(resolve,[$cnf( $equal(extension(X_13,X_12,X_13,X_12),reflection(X_13,X_12)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
equidistant(X_12,reflection(X_13,X_12),X_13,X_12),
inference(resolve,[$cnf( equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
equidistant(X_20,reflection(X_20,X_20),X_20,X_20),
inference(subst,[],[refute_0_21:[bind(X_12,$fot(X_20)),bind(X_13,$fot(X_20))]]) ).
cnf(refute_0_23,plain,
( ~ equidistant(X_20,reflection(X_20,X_20),X_20,X_20)
| X_20 = reflection(X_20,X_20) ),
inference(subst,[],[identity_for_equidistance:[bind(X,$fot(X_20)),bind(Y,$fot(reflection(X_20,X_20))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_24,plain,
X_20 = reflection(X_20,X_20),
inference(resolve,[$cnf( equidistant(X_20,reflection(X_20,X_20),X_20,X_20) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( X_20 != reflection(X_20,X_20)
| reflection(X_20,X_20) = X_20 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_20)),bind(Y0,$fot(reflection(X_20,X_20)))]]) ).
cnf(refute_0_26,plain,
reflection(X_20,X_20) = X_20,
inference(resolve,[$cnf( $equal(X_20,reflection(X_20,X_20)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
reflection(u,u) = u,
inference(subst,[],[refute_0_26:[bind(X_20,$fot(u))]]) ).
cnf(refute_0_28,plain,
( reflection(u,u) != u
| u != u
| u = reflection(u,u) ),
introduced(tautology,[equality,[$cnf( ~ $equal(u,reflection(u,u)) ),[1],$fot(u)]]) ).
cnf(refute_0_29,plain,
( u != u
| u = reflection(u,u) ),
inference(resolve,[$cnf( $equal(reflection(u,u),u) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
u != u,
inference(resolve,[$cnf( $equal(u,reflection(u,u)) )],[refute_0_29,refute_0_14]) ).
cnf(refute_0_31,plain,
u = u,
introduced(tautology,[refl,[$fot(u)]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( $equal(u,u) )],[refute_0_31,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO056-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 16:50:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.38
%------------------------------------------------------------------------------