TSTP Solution File: SET787-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET787-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 : Tue Jul 19 03:37:13 EDT 2022

% Result   : Unsatisfiable 0.19s 0.46s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   31 (  10 unt;  11 nHn;  21 RR)
%            Number of literals    :   60 (  13 equ;  20 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   27 (  12 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause119,axiom,
    ( ~ member(U,union(V))
    | member(U,unionE_sk1(U,V)) ) ).

cnf(clause120,axiom,
    ( ~ member(U,union(V))
    | member(unionE_sk1(U,V),V) ) ).

cnf(clause112,axiom,
    ( ~ member(U,cons(V,W))
    | U = V
    | member(U,W) ) ).

cnf(unI1,axiom,
    ( ~ member(C,A)
    | member(C,un(A,B)) ) ).

cnf(unI2,axiom,
    ( ~ member(C,B)
    | member(C,un(A,B)) ) ).

cnf(clause158,axiom,
    ~ member(X,eptset) ).

cnf(un_eq_Union_2_c1,negated_conjecture,
    member(sk2,union(cons(a,cons(b,eptset)))) ).

cnf(un_eq_Union_2_c2,negated_conjecture,
    ~ member(sk2,un(a,b)) ).

cnf(refute_0_0,plain,
    ( ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) ),
    inference(subst,[],[clause119:[bind(U,$fot(sk2)),bind(V,$fot(cons(a,cons(b,eptset))))]]) ).

cnf(refute_0_1,plain,
    member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
    inference(resolve,[$cnf( member(sk2,union(cons(a,cons(b,eptset)))) )],[un_eq_Union_2_c1,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X_12)) ),
    inference(subst,[],[unI1:[bind(A,$fot(unionE_sk1(sk2,cons(a,cons(b,eptset))))),bind(B,$fot(X_12)),bind(C,$fot(sk2))]]) ).

cnf(refute_0_3,plain,
    member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X_12)),
    inference(resolve,[$cnf( member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset))))
    | member(sk2,un(X_23,unionE_sk1(sk2,cons(a,cons(b,eptset))))) ),
    inference(subst,[],[unI2:[bind(A,$fot(X_23)),bind(B,$fot(unionE_sk1(sk2,cons(a,cons(b,eptset))))),bind(C,$fot(sk2))]]) ).

cnf(refute_0_5,plain,
    member(sk2,un(X_23,unionE_sk1(sk2,cons(a,cons(b,eptset))))),
    inference(resolve,[$cnf( member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
    | unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset) ),
    inference(subst,[],[clause112:[bind(U,$fot(unionE_sk1(sk2,cons(a,cons(b,eptset))))),bind(V,$fot(b)),bind(W,$fot(eptset))]]) ).

cnf(refute_0_7,plain,
    ( ~ member(sk2,union(cons(a,cons(b,eptset))))
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) ),
    inference(subst,[],[clause120:[bind(U,$fot(sk2)),bind(V,$fot(cons(a,cons(b,eptset))))]]) ).

cnf(refute_0_8,plain,
    member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
    inference(resolve,[$cnf( member(sk2,union(cons(a,cons(b,eptset)))) )],[un_eq_Union_2_c1,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset)))
    | unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
    inference(subst,[],[clause112:[bind(U,$fot(unionE_sk1(sk2,cons(a,cons(b,eptset))))),bind(V,$fot(a)),bind(W,$fot(cons(b,eptset)))]]) ).

cnf(refute_0_10,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
    inference(resolve,[$cnf( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
    | member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset) ),
    inference(resolve,[$cnf( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) )],[refute_0_10,refute_0_6]) ).

cnf(refute_0_12,plain,
    ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset),
    inference(subst,[],[clause158:[bind(X,$fot(unionE_sk1(sk2,cons(a,cons(b,eptset)))))]]) ).

cnf(refute_0_13,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | unionE_sk1(sk2,cons(a,cons(b,eptset))) = b ),
    inference(resolve,[$cnf( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != b
    | ~ member(sk2,un(X_23,unionE_sk1(sk2,cons(a,cons(b,eptset)))))
    | member(sk2,un(X_23,b)) ),
    introduced(tautology,[equality,[$cnf( member(sk2,un(X_23,unionE_sk1(sk2,cons(a,cons(b,eptset))))) ),[1,1],$fot(b)]]) ).

cnf(refute_0_15,plain,
    ( ~ member(sk2,un(X_23,unionE_sk1(sk2,cons(a,cons(b,eptset)))))
    | unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(sk2,un(X_23,b)) ),
    inference(resolve,[$cnf( $equal(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(sk2,un(X_23,b)) ),
    inference(resolve,[$cnf( member(sk2,un(X_23,unionE_sk1(sk2,cons(a,cons(b,eptset))))) )],[refute_0_5,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
    | member(sk2,un(X_285,b)) ),
    inference(subst,[],[refute_0_16:[bind(X_23,$fot(X_285))]]) ).

cnf(refute_0_18,plain,
    ( unionE_sk1(sk2,cons(a,cons(b,eptset))) != a
    | ~ member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X_12))
    | member(sk2,un(a,X_12)) ),
    introduced(tautology,[equality,[$cnf( member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X_12)) ),[1,0],$fot(a)]]) ).

cnf(refute_0_19,plain,
    ( ~ member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X_12))
    | member(sk2,un(X_285,b))
    | member(sk2,un(a,X_12)) ),
    inference(resolve,[$cnf( $equal(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( member(sk2,un(X_285,b))
    | member(sk2,un(a,X_12)) ),
    inference(resolve,[$cnf( member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X_12)) )],[refute_0_3,refute_0_19]) ).

cnf(refute_0_21,plain,
    member(sk2,un(a,b)),
    inference(subst,[],[refute_0_20:[bind(X_12,$fot(b)),bind(X_285,$fot(a))]]) ).

cnf(refute_0_22,plain,
    $false,
    inference(resolve,[$cnf( member(sk2,un(a,b)) )],[refute_0_21,un_eq_Union_2_c2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET787-1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n029.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 : Sun Jul 10 02:44:16 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.46  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46  
% 0.19/0.46  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.47  
%------------------------------------------------------------------------------