TSTP Solution File: SET863-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 03:37:57 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 14
% Syntax : Number of clauses : 74 ( 12 unt; 38 nHn; 52 RR)
% Number of literals : 202 ( 0 equ; 83 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Zorn_Ochain__extend_0,axiom,
( ~ c_in(V_z,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_c,tc_set(T_a))
| c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_Ochain__extend_1,axiom,
( ~ c_in(V_z,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_z,tc_set(T_a))
| c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_Omaxchain__super__lemma_0,axiom,
( ~ c_in(V_z,V_x,T_a)
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(V_z,V_y,T_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a)) ) ).
cnf(cls_Zorn_Omaxchain__super__lemma_1,axiom,
( ~ c_in(V_z,V_x,T_a)
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))
| c_in(V_z,V_y,T_a) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)) ).
cnf(cls_conjecture_4,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)) ).
cnf(cls_conjecture_5,negated_conjecture,
c_in(v_xa,v_x,t_a) ).
cnf(cls_conjecture_6,negated_conjecture,
~ c_in(v_xa,v_y,t_a) ).
cnf(cls_conjecture_7,negated_conjecture,
( c_lessequals(V_U,v_y,tc_set(t_a))
| ~ c_in(V_U,v_c,tc_set(t_a)) ) ).
cnf(refute_0_0,plain,
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_123,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X_123,t_a),v_y,tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_7:[bind(V_U,$fot(c_Zorn_Omaxchain__super__lemma__1(v_c,X_123,t_a)))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(V_z,v_x,t_a)
| ~ c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(V_z,V_y,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,V_y,t_a),v_c,tc_set(t_a)) ),
inference(subst,[],[cls_Zorn_Omaxchain__super__lemma_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_c,$fot(v_c)),bind(V_x,$fot(v_x))]]) ).
cnf(refute_0_2,plain,
( ~ c_in(v_c,c_Zorn_Ochain(V_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,V_S,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(V_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_Ochain__extend_1:[bind(T_a,$fot(t_a)),bind(V_c,$fot(v_c)),bind(V_z,$fot(v_x))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),v_x,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(t_a)),bind(V_A,$fot(c_Zorn_Ochain__extend__1(v_c,v_x,t_a))),bind(V_B,$fot(v_x))]]) ).
cnf(refute_0_4,plain,
( ~ c_in(X_13,v_y,t_a)
| ~ c_lessequals(v_y,v_x,tc_set(t_a))
| c_in(X_13,v_x,t_a) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_y)),bind(V_B,$fot(v_x)),bind(V_c,$fot(X_13))]]) ).
cnf(refute_0_5,plain,
( ~ c_in(X_13,v_y,t_a)
| c_in(X_13,v_x,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_y,v_x,tc_set(t_a)) )],[cls_conjecture_4,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,t_a),v_y,t_a)
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,t_a),v_x,t_a) ),
inference(subst,[],[refute_0_5:[bind(X_13,$fot(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,t_a)))]]) ).
cnf(refute_0_7,plain,
( c_in(c_Main_OsubsetI__1(X_11,V_B,X_10),X_11,X_10)
| c_lessequals(X_11,V_B,tc_set(X_10)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_10)),bind(V_A,$fot(X_11))]]) ).
cnf(refute_0_8,plain,
( ~ c_in(c_Main_OsubsetI__1(X_11,V_B,X_10),X_11,X_10)
| ~ c_lessequals(X_11,X_12,tc_set(X_10))
| c_in(c_Main_OsubsetI__1(X_11,V_B,X_10),X_12,X_10) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(X_10)),bind(V_A,$fot(X_11)),bind(V_B,$fot(X_12)),bind(V_c,$fot(c_Main_OsubsetI__1(X_11,V_B,X_10)))]]) ).
cnf(refute_0_9,plain,
( ~ c_lessequals(X_11,X_12,tc_set(X_10))
| c_in(c_Main_OsubsetI__1(X_11,V_B,X_10),X_12,X_10)
| c_lessequals(X_11,V_B,tc_set(X_10)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_11,V_B,X_10),X_11,X_10) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),V_B,t_a),v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),V_B,tc_set(t_a)) ),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(t_a)),bind(X_11,$fot(c_Zorn_Ochain__extend__1(v_c,v_x,t_a))),bind(X_12,$fot(v_y))]]) ).
cnf(refute_0_11,plain,
( ~ c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_7:[bind(V_U,$fot(c_Zorn_Ochain__extend__1(v_c,v_x,t_a)))]]) ).
cnf(refute_0_12,plain,
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_70,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X_70,t_a),v_y,tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_7:[bind(V_U,$fot(c_Zorn_Omaxchain__super__lemma__1(v_c,X_70,t_a)))]]) ).
cnf(refute_0_13,plain,
( ~ c_in(X_37,v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,X_37,t_a),v_c,tc_set(t_a))
| c_in(c_union(c_insert(X_37,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_Ochain__extend_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_c,$fot(v_c)),bind(V_z,$fot(X_37))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(X_37,v_S,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,X_37,t_a),v_c,tc_set(t_a))
| c_in(c_union(c_insert(X_37,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ c_in(v_x,v_S,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_14:[bind(X_37,$fot(v_x))]]) ).
cnf(refute_0_16,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,v_S,tc_set(t_a)) )],[cls_conjecture_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ c_in(X_67,v_x,t_a)
| ~ c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(X_67,X_66,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_66,t_a),v_c,tc_set(t_a)) ),
inference(subst,[],[cls_Zorn_Omaxchain__super__lemma_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_c,$fot(v_c)),bind(V_x,$fot(v_x)),bind(V_y,$fot(X_66)),bind(V_z,$fot(X_67))]]) ).
cnf(refute_0_18,plain,
( ~ c_in(X_67,v_x,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(X_67,X_66,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_66,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ c_in(X_67,v_x,t_a)
| c_in(X_67,X_66,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_66,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ c_in(v_xa,v_x,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_68,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X_68,t_a) ),
inference(subst,[],[refute_0_19:[bind(X_66,$fot(X_68)),bind(X_67,$fot(v_xa))]]) ).
cnf(refute_0_21,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_68,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X_68,t_a) ),
inference(resolve,[$cnf( c_in(v_xa,v_x,t_a) )],[cls_conjecture_5,refute_0_20]) ).
cnf(refute_0_22,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_70,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X_70,t_a) ),
inference(subst,[],[refute_0_21:[bind(X_68,$fot(X_70))]]) ).
cnf(refute_0_23,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X_70,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X_70,t_a),v_y,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_70,t_a),v_c,tc_set(t_a)) )],[refute_0_22,refute_0_12]) ).
cnf(refute_0_24,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(subst,[],[refute_0_23:[bind(X_70,$fot(v_y))]]) ).
cnf(refute_0_25,plain,
( ~ c_in(X_108,v_x,t_a)
| ~ c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X_107,t_a),X_107,tc_set(t_a))
| c_in(X_108,X_107,t_a) ),
inference(subst,[],[cls_Zorn_Omaxchain__super__lemma_1:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_c,$fot(v_c)),bind(V_x,$fot(v_x)),bind(V_y,$fot(X_107)),bind(V_z,$fot(X_108))]]) ).
cnf(refute_0_26,plain,
( ~ c_in(X_108,v_x,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X_107,t_a),X_107,tc_set(t_a))
| c_in(X_108,X_107,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ c_in(X_108,v_x,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X_107,t_a),X_107,tc_set(t_a))
| c_in(X_108,X_107,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ c_in(X_110,v_x,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| c_in(X_110,v_y,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
inference(subst,[],[refute_0_27:[bind(X_107,$fot(v_y)),bind(X_108,$fot(X_110))]]) ).
cnf(refute_0_29,plain,
( ~ c_in(X_110,v_x,t_a)
| c_in(X_110,v_y,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ c_in(X_110,v_x,t_a)
| c_in(X_110,v_y,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(v_xa,v_y,t_a) )],[refute_0_29,cls_conjecture_6]) ).
cnf(refute_0_31,plain,
( ~ c_in(v_xa,v_x,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(subst,[],[refute_0_30:[bind(X_110,$fot(v_xa))]]) ).
cnf(refute_0_32,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolve,[$cnf( c_in(v_xa,v_x,t_a) )],[cls_conjecture_5,refute_0_31]) ).
cnf(refute_0_33,plain,
c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)),
inference(resolve,[$cnf( c_in(v_xa,v_y,t_a) )],[refute_0_32,cls_conjecture_6]) ).
cnf(refute_0_34,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,tc_set(t_a)),
inference(resolve,[$cnf( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) )],[refute_0_33,refute_0_11]) ).
cnf(refute_0_35,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),V_B,t_a),v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),V_B,tc_set(t_a)) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,tc_set(t_a)) )],[refute_0_34,refute_0_10]) ).
cnf(refute_0_36,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,t_a),v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,tc_set(t_a)) ),
inference(subst,[],[refute_0_35:[bind(V_B,$fot(X_114))]]) ).
cnf(refute_0_37,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,t_a),v_x,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X_114,t_a),v_y,t_a) )],[refute_0_36,refute_0_6]) ).
cnf(refute_0_38,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),v_x,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)) ),
inference(subst,[],[refute_0_37:[bind(X_114,$fot(v_x))]]) ).
cnf(refute_0_39,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),v_x,t_a) )],[refute_0_38,refute_0_3]) ).
cnf(refute_0_40,plain,
( ~ c_in(v_c,c_Zorn_Ochain(V_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,V_S,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(V_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)) )],[refute_0_39,refute_0_2]) ).
cnf(refute_0_41,plain,
( ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_S,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_40:[bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_42,plain,
( ~ c_in(v_x,v_S,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_41]) ).
cnf(refute_0_43,plain,
c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(v_x,v_S,tc_set(t_a)) )],[cls_conjecture_3,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ c_in(V_z,v_x,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(V_z,V_y,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,V_y,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_43,refute_0_1]) ).
cnf(refute_0_45,plain,
( ~ c_in(V_z,v_x,t_a)
| c_in(V_z,V_y,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,V_y,t_a),v_c,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ c_in(v_xa,v_x,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_121,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X_121,t_a) ),
inference(subst,[],[refute_0_45:[bind(V_y,$fot(X_121)),bind(V_z,$fot(v_xa))]]) ).
cnf(refute_0_47,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_121,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X_121,t_a) ),
inference(resolve,[$cnf( c_in(v_xa,v_x,t_a) )],[cls_conjecture_5,refute_0_46]) ).
cnf(refute_0_48,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_123,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X_123,t_a) ),
inference(subst,[],[refute_0_47:[bind(X_121,$fot(X_123))]]) ).
cnf(refute_0_49,plain,
( c_in(v_xa,X_123,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X_123,t_a),v_y,tc_set(t_a)) ),
inference(resolve,[$cnf( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X_123,t_a),v_c,tc_set(t_a)) )],[refute_0_48,refute_0_0]) ).
cnf(refute_0_50,plain,
( c_in(v_xa,v_y,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(subst,[],[refute_0_49:[bind(X_123,$fot(v_y))]]) ).
cnf(refute_0_51,plain,
( ~ c_in(V_z,v_x,t_a)
| ~ c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,V_y,t_a),V_y,tc_set(t_a))
| c_in(V_z,V_y,t_a) ),
inference(subst,[],[cls_Zorn_Omaxchain__super__lemma_1:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_c,$fot(v_c)),bind(V_x,$fot(v_x))]]) ).
cnf(refute_0_52,plain,
( ~ c_in(V_z,v_x,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,V_y,t_a),V_y,tc_set(t_a))
| c_in(V_z,V_y,t_a) ),
inference(resolve,[$cnf( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_43,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ c_in(V_z,v_x,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,V_y,t_a),V_y,tc_set(t_a))
| c_in(V_z,V_y,t_a) ),
inference(resolve,[$cnf( c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ c_in(X_127,v_x,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| c_in(X_127,v_y,t_a) ),
inference(subst,[],[refute_0_53:[bind(V_y,$fot(v_y)),bind(V_z,$fot(X_127))]]) ).
cnf(refute_0_55,plain,
( ~ c_in(X_127,v_x,t_a)
| c_in(X_127,v_y,t_a)
| c_in(v_xa,v_y,t_a) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) )],[refute_0_50,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ c_in(X_127,v_x,t_a)
| c_in(X_127,v_y,t_a) ),
inference(resolve,[$cnf( c_in(v_xa,v_y,t_a) )],[refute_0_55,cls_conjecture_6]) ).
cnf(refute_0_57,plain,
( ~ c_in(v_xa,v_x,t_a)
| c_in(v_xa,v_y,t_a) ),
inference(subst,[],[refute_0_56:[bind(X_127,$fot(v_xa))]]) ).
cnf(refute_0_58,plain,
c_in(v_xa,v_y,t_a),
inference(resolve,[$cnf( c_in(v_xa,v_x,t_a) )],[cls_conjecture_5,refute_0_57]) ).
cnf(refute_0_59,plain,
$false,
inference(resolve,[$cnf( c_in(v_xa,v_y,t_a) )],[refute_0_58,cls_conjecture_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n013.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 : Mon Jul 11 07:17:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43
% 0.19/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.44
%------------------------------------------------------------------------------