TSTP Solution File: GEO040-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO040-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 05:23:47 EDT 2022
% Result : Unsatisfiable 25.11s 25.34s
% Output : CNFRefutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 12 unt; 0 nHn; 28 RR)
% Number of literals : 52 ( 19 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_for_betweeness,axiom,
( ~ between(X,Y,X)
| X = Y ) ).
cnf(inner_pasch1,axiom,
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(V,inner_pasch(U,V,W,X,Y),Y) ) ).
cnf(inner_pasch2,axiom,
( ~ between(U,V,W)
| ~ between(Y,X,W)
| between(X,inner_pasch(U,V,W,X,Y),U) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_between_v_and_w,hypothesis,
between(v,u,w) ).
cnf(prove_u_is_v,negated_conjecture,
u != v ).
cnf(refute_0_0,plain,
( ~ between(v,u,v)
| v = u ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(v)),bind(Y,$fot(u))]]) ).
cnf(refute_0_1,plain,
( ~ between(X_395,X_396,w)
| ~ between(u,v,w)
| between(v,inner_pasch(X_395,X_396,w,v,u),X_395) ),
inference(subst,[],[inner_pasch2:[bind(U,$fot(X_395)),bind(V,$fot(X_396)),bind(W,$fot(w)),bind(X,$fot(v)),bind(Y,$fot(u))]]) ).
cnf(refute_0_2,plain,
( ~ between(X_395,X_396,w)
| between(v,inner_pasch(X_395,X_396,w,v,u),X_395) ),
inference(resolve,[$cnf( between(u,v,w) )],[v_between_u_and_w,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ between(v,u,w)
| between(v,inner_pasch(v,u,w,v,u),v) ),
inference(subst,[],[refute_0_2:[bind(X_395,$fot(v)),bind(X_396,$fot(u))]]) ).
cnf(refute_0_4,plain,
between(v,inner_pasch(v,u,w,v,u),v),
inference(resolve,[$cnf( between(v,u,w) )],[u_between_v_and_w,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ between(u,inner_pasch(v,u,w,v,u),u)
| u = inner_pasch(v,u,w,v,u) ),
inference(subst,[],[identity_for_betweeness:[bind(X,$fot(u)),bind(Y,$fot(inner_pasch(v,u,w,v,u)))]]) ).
cnf(refute_0_6,plain,
( ~ between(X_88,X_89,w)
| ~ between(u,v,w)
| between(X_89,inner_pasch(X_88,X_89,w,v,u),u) ),
inference(subst,[],[inner_pasch1:[bind(U,$fot(X_88)),bind(V,$fot(X_89)),bind(W,$fot(w)),bind(X,$fot(v)),bind(Y,$fot(u))]]) ).
cnf(refute_0_7,plain,
( ~ between(X_88,X_89,w)
| between(X_89,inner_pasch(X_88,X_89,w,v,u),u) ),
inference(resolve,[$cnf( between(u,v,w) )],[v_between_u_and_w,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ between(v,u,w)
| between(u,inner_pasch(v,u,w,v,u),u) ),
inference(subst,[],[refute_0_7:[bind(X_88,$fot(v)),bind(X_89,$fot(u))]]) ).
cnf(refute_0_9,plain,
between(u,inner_pasch(v,u,w,v,u),u),
inference(resolve,[$cnf( between(v,u,w) )],[u_between_v_and_w,refute_0_8]) ).
cnf(refute_0_10,plain,
u = inner_pasch(v,u,w,v,u),
inference(resolve,[$cnf( between(u,inner_pasch(v,u,w,v,u),u) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( u != inner_pasch(v,u,w,v,u)
| inner_pasch(v,u,w,v,u) = u ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(u)),bind(Y0,$fot(inner_pasch(v,u,w,v,u)))]]) ).
cnf(refute_0_15,plain,
inner_pasch(v,u,w,v,u) = u,
inference(resolve,[$cnf( $equal(u,inner_pasch(v,u,w,v,u)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( inner_pasch(v,u,w,v,u) != u
| ~ between(v,inner_pasch(v,u,w,v,u),v)
| between(v,u,v) ),
introduced(tautology,[equality,[$cnf( between(v,inner_pasch(v,u,w,v,u),v) ),[1],$fot(u)]]) ).
cnf(refute_0_17,plain,
( ~ between(v,inner_pasch(v,u,w,v,u),v)
| between(v,u,v) ),
inference(resolve,[$cnf( $equal(inner_pasch(v,u,w,v,u),u) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
between(v,u,v),
inference(resolve,[$cnf( between(v,inner_pasch(v,u,w,v,u),v) )],[refute_0_4,refute_0_17]) ).
cnf(refute_0_19,plain,
v = u,
inference(resolve,[$cnf( between(v,u,v) )],[refute_0_18,refute_0_0]) ).
cnf(refute_0_20,plain,
( v != u
| u = v ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(v)),bind(Y0,$fot(u))]]) ).
cnf(refute_0_21,plain,
v != u,
inference(resolve,[$cnf( $equal(u,v) )],[refute_0_20,prove_u_is_v]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( $equal(v,u) )],[refute_0_19,refute_0_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO040-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 18:57:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 25.11/25.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.11/25.34
% 25.11/25.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.11/25.34
%------------------------------------------------------------------------------