TSTP Solution File: SET865-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 03:37:59 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 12 unt; 0 nHn; 25 RR)
% Number of literals : 53 ( 6 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
( c_in(c_Union(V_U,t_a),v_S,tc_set(t_a))
| ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_in(v_x(V_U),v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( V_U != v_x(V_U)
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
cnf(cls_Set_OsubsetD_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ) ).
cnf(cls_Zorn_OHausdorff_0,axiom,
c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) ).
cnf(cls_Zorn_Omaxchain__Zorn_0,axiom,
( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| c_Union(V_c,T_a) = V_u ) ).
cnf(cls_Zorn_Omaxchain__subset__chain_0,axiom,
c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ).
cnf(refute_0_0,plain,
( ~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a))
| c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(c_Zorn_OHausdorff__1(v_S,t_a)))]]) ).
cnf(refute_0_2,plain,
c_lessequals(c_Zorn_Omaxchain(X_13,X_12),c_Zorn_Ochain(X_13,X_12),tc_set(tc_set(tc_set(X_12)))),
inference(subst,[],[cls_Zorn_Omaxchain__subset__chain_0:[bind(T_a,$fot(X_12)),bind(V_S,$fot(X_13))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Omaxchain(V_S,T_a),X_10,tc_set(tc_set(tc_set(T_a))))
| c_in(c_Zorn_OHausdorff__1(V_S,T_a),X_10,tc_set(tc_set(T_a))) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(tc_set(tc_set(T_a)))),bind(V_A,$fot(c_Zorn_Omaxchain(V_S,T_a))),bind(V_B,$fot(X_10)),bind(V_c,$fot(c_Zorn_OHausdorff__1(V_S,T_a)))]]) ).
cnf(refute_0_4,plain,
( ~ c_lessequals(c_Zorn_Omaxchain(V_S,T_a),X_10,tc_set(tc_set(tc_set(T_a))))
| c_in(c_Zorn_OHausdorff__1(V_S,T_a),X_10,tc_set(tc_set(T_a))) ),
inference(resolve,[$cnf( c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) )],[cls_Zorn_OHausdorff_0,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ c_lessequals(c_Zorn_Omaxchain(X_13,X_12),c_Zorn_Ochain(X_13,X_12),tc_set(tc_set(tc_set(X_12))))
| c_in(c_Zorn_OHausdorff__1(X_13,X_12),c_Zorn_Ochain(X_13,X_12),tc_set(tc_set(X_12))) ),
inference(subst,[],[refute_0_4:[bind(T_a,$fot(X_12)),bind(V_S,$fot(X_13)),bind(X_10,$fot(c_Zorn_Ochain(X_13,X_12)))]]) ).
cnf(refute_0_6,plain,
c_in(c_Zorn_OHausdorff__1(X_13,X_12),c_Zorn_Ochain(X_13,X_12),tc_set(tc_set(X_12))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Omaxchain(X_13,X_12),c_Zorn_Ochain(X_13,X_12),tc_set(tc_set(tc_set(X_12)))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(subst,[],[refute_0_6:[bind(X_12,$fot(t_a)),bind(X_13,$fot(v_S))]]) ).
cnf(refute_0_8,plain,
c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
inference(resolve,[$cnf( c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)),
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( ~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a))
| c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)))]]) ).
cnf(refute_0_11,plain,
c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)),
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(X_38,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),X_38,tc_set(t_a))
| ~ c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a))
| c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) ),
inference(subst,[],[cls_Zorn_Omaxchain__Zorn_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(X_38)),bind(V_c,$fot(c_Zorn_OHausdorff__1(v_S,t_a))),bind(V_u,$fot(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a))))]]) ).
cnf(refute_0_13,plain,
( ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(X_38,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),X_38,tc_set(t_a))
| c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) ),
inference(resolve,[$cnf( c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) != v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a))
| ~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_3:[bind(V_U,$fot(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)))]]) ).
cnf(refute_0_15,plain,
c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) != v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(X_38,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),X_38,tc_set(t_a)) ),
inference(resolve,[$cnf( $equal(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a))) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)) ),
inference(subst,[],[refute_0_16:[bind(X_38,$fot(v_S))]]) ).
cnf(refute_0_18,plain,
~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)) )],[refute_0_9,refute_0_17]) ).
cnf(refute_0_19,plain,
c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(subst,[],[cls_Zorn_OHausdorff_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_19,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.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 : Sat Jul 9 17:40:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39
%------------------------------------------------------------------------------