%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO059-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 1.53s 1.68s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 41 ( 24 unt; 0 nHn; 20 RR)
% Number of literals : 64 ( 12 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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 : 97 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflexivity_for_equidistance,axiom,
equidistant(X,Y,Y,X) ).
cnf(transitivity_for_equidistance,axiom,
( ~ equidistant(X,Y,Z,V)
| ~ equidistant(X,Y,V2,W)
| equidistant(Z,V,V2,W) ) ).
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(prove_congruence,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)) ).
cnf(refute_0_0,plain,
equidistant(X_997,X_1002,X_1002,X_997),
inference(subst,[],[reflexivity_for_equidistance:[bind(X,$fot(X_997)),bind(Y,$fot(X_1002))]]) ).
cnf(refute_0_1,plain,
( ~ equidistant(X_997,X_1002,X_1002,X_997)
| ~ equidistant(X_997,X_1002,X_998,X_999)
| equidistant(X_1002,X_997,X_998,X_999) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_997)),bind(V2,$fot(X_998)),bind(W,$fot(X_999)),bind(X,$fot(X_997)),bind(Y,$fot(X_1002)),bind(Z,$fot(X_1002))]]) ).
cnf(refute_0_2,plain,
( ~ equidistant(X_997,X_1002,X_998,X_999)
| equidistant(X_1002,X_997,X_998,X_999) ),
inference(resolve,[$cnf( equidistant(X_997,X_1002,X_1002,X_997) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ equidistant(X_1071,X_1072,X_1072,reflection(reflection(X_1071,X_1072),X_1072))
| equidistant(X_1072,X_1071,X_1072,reflection(reflection(X_1071,X_1072),X_1072)) ),
inference(subst,[],[refute_0_2:[bind(X_1002,$fot(X_1072)),bind(X_997,$fot(X_1071)),bind(X_998,$fot(X_1072)),bind(X_999,$fot(reflection(reflection(X_1071,X_1072),X_1072)))]]) ).
cnf(refute_0_4,plain,
( ~ equidistant(X_1019,X_1020,X_1020,reflection(X_1019,X_1020))
| equidistant(X_1020,X_1019,X_1020,reflection(X_1019,X_1020)) ),
inference(subst,[],[refute_0_2:[bind(X_1002,$fot(X_1020)),bind(X_997,$fot(X_1019)),bind(X_998,$fot(X_1020)),bind(X_999,$fot(reflection(X_1019,X_1020)))]]) ).
cnf(refute_0_5,plain,
equidistant(X_12,extension(X_13,X_12,X_13,X_12),X_13,X_12),
inference(subst,[],[segment_construction2:[bind(V,$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(X_1014,reflection(X_1013,X_1014),X_1013,X_1014),
inference(subst,[],[refute_0_14:[bind(X_12,$fot(X_1014)),bind(X_13,$fot(X_1013))]]) ).
cnf(refute_0_16,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,$fot(X_31))]]) ).
cnf(refute_0_17,plain,
( ~ equidistant(X_31,extension(X,X_31,X_33,X_30),X_33,X_30)
| equidistant(X_33,X_30,X_33,X_30) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$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,$fot(X_33))]]) ).
cnf(refute_0_18,plain,
equidistant(X_33,X_30,X_33,X_30),
inference(resolve,[$cnf( equidistant(X_31,extension(X,X_31,X_33,X_30),X_33,X_30) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
equidistant(X_998,X_999,X_998,X_999),
inference(subst,[],[refute_0_18:[bind(X_30,$fot(X_999)),bind(X_33,$fot(X_998))]]) ).
cnf(refute_0_20,plain,
( ~ equidistant(X_998,X_999,X_1002,X_997)
| ~ equidistant(X_998,X_999,X_998,X_999)
| equidistant(X_1002,X_997,X_998,X_999) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_997)),bind(V2,$fot(X_998)),bind(W,$fot(X_999)),bind(X,$fot(X_998)),bind(Y,$fot(X_999)),bind(Z,$fot(X_1002))]]) ).
cnf(refute_0_21,plain,
( ~ equidistant(X_998,X_999,X_1002,X_997)
| equidistant(X_1002,X_997,X_998,X_999) ),
inference(resolve,[$cnf( equidistant(X_998,X_999,X_998,X_999) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ equidistant(X_1014,reflection(X_1013,X_1014),X_1013,X_1014)
| equidistant(X_1013,X_1014,X_1014,reflection(X_1013,X_1014)) ),
inference(subst,[],[refute_0_21:[bind(X_1002,$fot(X_1013)),bind(X_997,$fot(X_1014)),bind(X_998,$fot(X_1014)),bind(X_999,$fot(reflection(X_1013,X_1014)))]]) ).
cnf(refute_0_23,plain,
equidistant(X_1013,X_1014,X_1014,reflection(X_1013,X_1014)),
inference(resolve,[$cnf( equidistant(X_1014,reflection(X_1013,X_1014),X_1013,X_1014) )],[refute_0_15,refute_0_22]) ).
cnf(refute_0_24,plain,
equidistant(X_1019,X_1020,X_1020,reflection(X_1019,X_1020)),
inference(subst,[],[refute_0_23:[bind(X_1013,$fot(X_1019)),bind(X_1014,$fot(X_1020))]]) ).
cnf(refute_0_25,plain,
equidistant(X_1020,X_1019,X_1020,reflection(X_1019,X_1020)),
inference(resolve,[$cnf( equidistant(X_1019,X_1020,X_1020,reflection(X_1019,X_1020)) )],[refute_0_24,refute_0_4]) ).
cnf(refute_0_26,plain,
equidistant(X_1067,reflection(X_1065,X_1067),X_1067,reflection(reflection(X_1065,X_1067),X_1067)),
inference(subst,[],[refute_0_25:[bind(X_1019,$fot(reflection(X_1065,X_1067))),bind(X_1020,$fot(X_1067))]]) ).
cnf(refute_0_27,plain,
equidistant(X_997,reflection(X_1002,X_997),X_1002,X_997),
inference(subst,[],[refute_0_14:[bind(X_12,$fot(X_997)),bind(X_13,$fot(X_1002))]]) ).
cnf(refute_0_28,plain,
( ~ equidistant(X_997,reflection(X_1002,X_997),X_1002,X_997)
| ~ equidistant(X_997,reflection(X_1002,X_997),X_998,X_999)
| equidistant(X_1002,X_997,X_998,X_999) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_997)),bind(V2,$fot(X_998)),bind(W,$fot(X_999)),bind(X,$fot(X_997)),bind(Y,$fot(reflection(X_1002,X_997))),bind(Z,$fot(X_1002))]]) ).
cnf(refute_0_29,plain,
( ~ equidistant(X_997,reflection(X_1002,X_997),X_998,X_999)
| equidistant(X_1002,X_997,X_998,X_999) ),
inference(resolve,[$cnf( equidistant(X_997,reflection(X_1002,X_997),X_1002,X_997) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ equidistant(X_1067,reflection(X_1065,X_1067),X_1067,reflection(reflection(X_1065,X_1067),X_1067))
| equidistant(X_1065,X_1067,X_1067,reflection(reflection(X_1065,X_1067),X_1067)) ),
inference(subst,[],[refute_0_29:[bind(X_1002,$fot(X_1065)),bind(X_997,$fot(X_1067)),bind(X_998,$fot(X_1067)),bind(X_999,$fot(reflection(reflection(X_1065,X_1067),X_1067)))]]) ).
cnf(refute_0_31,plain,
equidistant(X_1065,X_1067,X_1067,reflection(reflection(X_1065,X_1067),X_1067)),
inference(resolve,[$cnf( equidistant(X_1067,reflection(X_1065,X_1067),X_1067,reflection(reflection(X_1065,X_1067),X_1067)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
equidistant(X_1071,X_1072,X_1072,reflection(reflection(X_1071,X_1072),X_1072)),
inference(subst,[],[refute_0_31:[bind(X_1065,$fot(X_1071)),bind(X_1067,$fot(X_1072))]]) ).
cnf(refute_0_33,plain,
equidistant(X_1072,X_1071,X_1072,reflection(reflection(X_1071,X_1072),X_1072)),
inference(resolve,[$cnf( equidistant(X_1071,X_1072,X_1072,reflection(reflection(X_1071,X_1072),X_1072)) )],[refute_0_32,refute_0_3]) ).
cnf(refute_0_34,plain,
equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(subst,[],[refute_0_33:[bind(X_1071,$fot(u)),bind(X_1072,$fot(v))]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( equidistant(v,u,v,reflection(reflection(u,v),v)) )],[refute_0_34,prove_congruence]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO059-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n016.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 23:51:36 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.53/1.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.53/1.68
% 1.53/1.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.53/1.69
%------------------------------------------------------------------------------