TSTP Solution File: GEO040-2 by Metis---2.4

View Problem - 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  
%------------------------------------------------------------------------------