%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO016-2 : 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 05:23:35 EDT 2022
% Result : Unsatisfiable 0.78s 0.94s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 8 unt; 0 nHn; 15 RR)
% Number of literals : 27 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 16 ( 0 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(u_to_v_equals_w_to_x,hypothesis,
equidistant(u,v,w,x) ).
cnf(prove_symmetry,negated_conjecture,
~ equidistant(v,u,w,x) ).
cnf(refute_0_0,plain,
( ~ equidistant(u,v,w,x)
| equidistant(w,x,w,x) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(x)),bind(V2,$fot(w)),bind(W,$fot(x)),bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(w))]]) ).
cnf(refute_0_1,plain,
equidistant(w,x,w,x),
inference(resolve,[$cnf( equidistant(u,v,w,x) )],[u_to_v_equals_w_to_x,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ equidistant(w,x,X_586,X_581)
| ~ equidistant(w,x,w,x)
| equidistant(X_586,X_581,w,x) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_581)),bind(V2,$fot(w)),bind(W,$fot(x)),bind(X,$fot(w)),bind(Y,$fot(x)),bind(Z,$fot(X_586))]]) ).
cnf(refute_0_3,plain,
( ~ equidistant(w,x,X_586,X_581)
| equidistant(X_586,X_581,w,x) ),
inference(resolve,[$cnf( equidistant(w,x,w,x) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ equidistant(w,x,v,u)
| equidistant(v,u,w,x) ),
inference(subst,[],[refute_0_3:[bind(X_581,$fot(u)),bind(X_586,$fot(v))]]) ).
cnf(refute_0_5,plain,
equidistant(u,v,v,u),
inference(subst,[],[reflexivity_for_equidistance:[bind(X,$fot(u)),bind(Y,$fot(v))]]) ).
cnf(refute_0_6,plain,
( ~ equidistant(u,v,X_582,X_583)
| ~ equidistant(u,v,w,x)
| equidistant(w,x,X_582,X_583) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(x)),bind(V2,$fot(X_582)),bind(W,$fot(X_583)),bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(w))]]) ).
cnf(refute_0_7,plain,
( ~ equidistant(u,v,X_582,X_583)
| equidistant(w,x,X_582,X_583) ),
inference(resolve,[$cnf( equidistant(u,v,w,x) )],[u_to_v_equals_w_to_x,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ equidistant(u,v,v,u)
| equidistant(w,x,v,u) ),
inference(subst,[],[refute_0_7:[bind(X_582,$fot(v)),bind(X_583,$fot(u))]]) ).
cnf(refute_0_9,plain,
equidistant(w,x,v,u),
inference(resolve,[$cnf( equidistant(u,v,v,u) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
equidistant(v,u,w,x),
inference(resolve,[$cnf( equidistant(w,x,v,u) )],[refute_0_9,refute_0_4]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( equidistant(v,u,w,x) )],[refute_0_10,prove_symmetry]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % 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 14:43:54 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.78/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.94
% 0.78/0.94 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.78/0.94
%------------------------------------------------------------------------------