TSTP Solution File: GEO022-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO022-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 05:23:39 EDT 2022
% Result : Unsatisfiable 0.67s 0.85s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 15 RR)
% Number of literals : 29 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 28 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
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(u_to_v_equals_w_to_x,hypothesis,
equidistant(u,v,w,x) ).
cnf(w_to_x_equals_y_to_z,hypothesis,
equidistant(w,x,y,z) ).
cnf(prove_transitivity,negated_conjecture,
~ equidistant(u,v,y,z) ).
cnf(refute_0_0,plain,
( ~ equidistant(w,x,X_544,X_539)
| ~ equidistant(w,x,y,z)
| equidistant(X_544,X_539,y,z) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_539)),bind(V2,$fot(y)),bind(W,$fot(z)),bind(X,$fot(w)),bind(Y,$fot(x)),bind(Z,$fot(X_544))]]) ).
cnf(refute_0_1,plain,
( ~ equidistant(w,x,X_544,X_539)
| equidistant(X_544,X_539,y,z) ),
inference(resolve,[$cnf( equidistant(w,x,y,z) )],[w_to_x_equals_y_to_z,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ equidistant(w,x,u,v)
| equidistant(u,v,y,z) ),
inference(subst,[],[refute_0_1:[bind(X_539,$fot(v)),bind(X_544,$fot(u))]]) ).
cnf(refute_0_3,plain,
equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22),
inference(subst,[],[segment_construction2:[bind(V,$fot(X_22)),bind(W,$fot(X_25)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_4,plain,
( ~ equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22)
| equidistant(X_25,X_22,X_25,X_22) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(X_22)),bind(V2,$fot(X_25)),bind(W,$fot(X_22)),bind(X,$fot(X_23)),bind(Y,$fot(extension(X,X_23,X_25,X_22))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_5,plain,
equidistant(X_25,X_22,X_25,X_22),
inference(resolve,[$cnf( equidistant(X_23,extension(X,X_23,X_25,X_22),X_25,X_22) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
equidistant(u,v,u,v),
inference(subst,[],[refute_0_5:[bind(X_22,$fot(v)),bind(X_25,$fot(u))]]) ).
cnf(refute_0_7,plain,
( ~ equidistant(u,v,X_540,X_541)
| ~ equidistant(u,v,w,x)
| equidistant(w,x,X_540,X_541) ),
inference(subst,[],[transitivity_for_equidistance:[bind(V,$fot(x)),bind(V2,$fot(X_540)),bind(W,$fot(X_541)),bind(X,$fot(u)),bind(Y,$fot(v)),bind(Z,$fot(w))]]) ).
cnf(refute_0_8,plain,
( ~ equidistant(u,v,X_540,X_541)
| equidistant(w,x,X_540,X_541) ),
inference(resolve,[$cnf( equidistant(u,v,w,x) )],[u_to_v_equals_w_to_x,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ equidistant(u,v,u,v)
| equidistant(w,x,u,v) ),
inference(subst,[],[refute_0_8:[bind(X_540,$fot(u)),bind(X_541,$fot(v))]]) ).
cnf(refute_0_10,plain,
equidistant(w,x,u,v),
inference(resolve,[$cnf( equidistant(u,v,u,v) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
equidistant(u,v,y,z),
inference(resolve,[$cnf( equidistant(w,x,u,v) )],[refute_0_10,refute_0_2]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( equidistant(u,v,y,z) )],[refute_0_11,prove_transitivity]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO022-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 17 19:28:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.67/0.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.85
% 0.67/0.85 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.67/0.85
%------------------------------------------------------------------------------