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