%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET857-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 03:37:53 EDT 2022
% Result : Unsatisfiable 30.38s 30.59s
% Output : CNFRefutation 30.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 19
% Syntax : Number of clauses : 89 ( 16 unt; 56 nHn; 65 RR)
% Number of literals : 289 ( 57 equ; 84 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 106 ( 8 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_OAbrial__axiom1_0,axiom,
c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ).
cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,V_V,t_a),V_U,tc_set(tc_set(t_a)))
| V_V = V_U
| ~ c_lessequals(V_V,V_U,tc_set(tc_set(t_a)))
| ~ c_in(V_V,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) ) ).
cnf(refute_0_0,plain,
( ~ c_in(X_138,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,X_138,tc_set(tc_set(t_a)))
| v_n = X_138
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X_138,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_conjecture_6:[bind(V_U,$fot(X_138)),bind(V_V,$fot(v_n))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(X_138,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,X_138,tc_set(tc_set(t_a)))
| v_n = X_138
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X_138,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_1:[bind(X_138,$fot(v_x))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_x)),bind(V_B,$fot(v_n))]]) ).
cnf(refute_0_4,plain,
( ~ c_in(c_Main_OsubsetI__1(X_55,X_52,tc_set(X_53)),c_Zorn_Osucc(X_54,X_55,X_53),tc_set(X_53))
| ~ c_lessequals(c_Zorn_Osucc(X_54,X_55,X_53),V_B,tc_set(tc_set(X_53)))
| c_in(c_Main_OsubsetI__1(X_55,X_52,tc_set(X_53)),V_B,tc_set(X_53)) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(tc_set(X_53))),bind(V_A,$fot(c_Zorn_Osucc(X_54,X_55,X_53))),bind(V_c,$fot(c_Main_OsubsetI__1(X_55,X_52,tc_set(X_53))))]]) ).
cnf(refute_0_5,plain,
( c_in(c_Main_OsubsetI__1(X_19,V_B,tc_set(X_17)),X_19,tc_set(X_17))
| c_lessequals(X_19,V_B,tc_set(tc_set(X_17))) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(tc_set(X_17))),bind(V_A,$fot(X_19))]]) ).
cnf(refute_0_6,plain,
c_lessequals(X_12,c_Zorn_Osucc(V_S,X_12,T_a),tc_set(tc_set(T_a))),
inference(subst,[],[cls_Zorn_OAbrial__axiom1_0:[bind(V_x,$fot(X_12))]]) ).
cnf(refute_0_7,plain,
( ~ c_in(X_14,X_12,tc_set(T_a))
| ~ c_lessequals(X_12,c_Zorn_Osucc(V_S,X_12,T_a),tc_set(tc_set(T_a)))
| c_in(X_14,c_Zorn_Osucc(V_S,X_12,T_a),tc_set(T_a)) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(tc_set(T_a))),bind(V_A,$fot(X_12)),bind(V_B,$fot(c_Zorn_Osucc(V_S,X_12,T_a))),bind(V_c,$fot(X_14))]]) ).
cnf(refute_0_8,plain,
( ~ c_in(X_14,X_12,tc_set(T_a))
| c_in(X_14,c_Zorn_Osucc(V_S,X_12,T_a),tc_set(T_a)) ),
inference(resolve,[$cnf( c_lessequals(X_12,c_Zorn_Osucc(V_S,X_12,T_a),tc_set(tc_set(T_a))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ c_in(c_Main_OsubsetI__1(X_19,V_B,tc_set(X_17)),X_19,tc_set(X_17))
| c_in(c_Main_OsubsetI__1(X_19,V_B,tc_set(X_17)),c_Zorn_Osucc(X_18,X_19,X_17),tc_set(X_17)) ),
inference(subst,[],[refute_0_8:[bind(T_a,$fot(X_17)),bind(V_S,$fot(X_18)),bind(X_12,$fot(X_19)),bind(X_14,$fot(c_Main_OsubsetI__1(X_19,V_B,tc_set(X_17))))]]) ).
cnf(refute_0_10,plain,
( c_in(c_Main_OsubsetI__1(X_19,V_B,tc_set(X_17)),c_Zorn_Osucc(X_18,X_19,X_17),tc_set(X_17))
| c_lessequals(X_19,V_B,tc_set(tc_set(X_17))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_19,V_B,tc_set(X_17)),X_19,tc_set(X_17)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( c_in(c_Main_OsubsetI__1(X_55,X_52,tc_set(X_53)),c_Zorn_Osucc(X_54,X_55,X_53),tc_set(X_53))
| c_lessequals(X_55,X_52,tc_set(tc_set(X_53))) ),
inference(subst,[],[refute_0_10:[bind(V_B,$fot(X_52)),bind(X_17,$fot(X_53)),bind(X_18,$fot(X_54)),bind(X_19,$fot(X_55))]]) ).
cnf(refute_0_12,plain,
( ~ c_lessequals(c_Zorn_Osucc(X_54,X_55,X_53),V_B,tc_set(tc_set(X_53)))
| c_in(c_Main_OsubsetI__1(X_55,X_52,tc_set(X_53)),V_B,tc_set(X_53))
| c_lessequals(X_55,X_52,tc_set(tc_set(X_53))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_55,X_52,tc_set(X_53)),c_Zorn_Osucc(X_54,X_55,X_53),tc_set(X_53)) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(v_x,X_52,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_x,X_52,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_12:[bind(V_B,$fot(v_n)),bind(X_53,$fot(t_a)),bind(X_54,$fot(v_S)),bind(X_55,$fot(v_x))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(X_14,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
| c_in(X_14,c_Zorn_OTFin(v_S,t_a),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(v_Y)),bind(V_B,$fot(c_Zorn_OTFin(v_S,t_a))),bind(V_c,$fot(X_14))]]) ).
cnf(refute_0_15,plain,
( ~ c_in(X_14,v_Y,tc_set(tc_set(t_a)))
| c_in(X_14,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) )],[cls_conjecture_0,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_15:[bind(X_14,$fot(v_x))]]) ).
cnf(refute_0_17,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(v_x,v_Y,tc_set(tc_set(t_a))) )],[cls_conjecture_3,refute_0_16]) ).
cnf(refute_0_18,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X_281,t_a) != X_281
| ~ c_in(X_281,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_281,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X_281,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_2:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(X_281)),bind(V_n,$fot(v_n))]]) ).
cnf(refute_0_19,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X_281,t_a) != X_281
| ~ c_in(X_281,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_281,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X_281,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_18]) ).
cnf(refute_0_20,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_19:[bind(X_281,$fot(v_x))]]) ).
cnf(refute_0_21,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ c_in(V_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(V_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),V_n,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_3:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(v_x))]]) ).
cnf(refute_0_23,plain,
( ~ c_in(X_347,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X_347,t_a),X_347,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_347,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X_347,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_1:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(X_347)),bind(V_n,$fot(v_n))]]) ).
cnf(refute_0_24,plain,
( ~ c_in(X_347,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X_347,t_a),X_347,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_347,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X_347,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_24:[bind(X_347,$fot(v_x))]]) ).
cnf(refute_0_26,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_17,refute_0_25]) ).
cnf(refute_0_27,plain,
( c_in(c_Main_OsubsetI__1(v_x,X_52,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_52,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) )],[refute_0_26,refute_0_13]) ).
cnf(refute_0_28,plain,
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),V_U,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = V_U
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),V_U,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_conjecture_6:[bind(V_V,$fot(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a)))]]) ).
cnf(refute_0_29,plain,
( ~ c_in(X_407,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_407,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X_407,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(v_x)),bind(V_n,$fot(X_407))]]) ).
cnf(refute_0_30,plain,
( ~ c_in(X_407,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_407,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X_407,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_17,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_30:[bind(X_407,$fot(v_n))]]) ).
cnf(refute_0_32,plain,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),V_U,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = V_U
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),V_U,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_32,refute_0_28]) ).
cnf(refute_0_34,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_33:[bind(V_U,$fot(v_x))]]) ).
cnf(refute_0_35,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_52,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_52,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_27,refute_0_34]) ).
cnf(refute_0_36,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_52,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_52,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,v_Y,tc_set(tc_set(t_a))) )],[cls_conjecture_3,refute_0_35]) ).
cnf(refute_0_37,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_1033,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_1033,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_36:[bind(X_52,$fot(X_1033))]]) ).
cnf(refute_0_38,plain,
( ~ c_in(V_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_1033,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(V_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),V_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_1033,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_37,refute_0_22]) ).
cnf(refute_0_39,plain,
( ~ c_in(V_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_1033,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(V_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),V_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_1033,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_17,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_6707,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_6707,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_39:[bind(V_n,$fot(v_n)),bind(X_1033,$fot(X_6707))]]) ).
cnf(refute_0_41,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_6707,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_6707,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_40]) ).
cnf(refute_0_42,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_6708,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_6708,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_41:[bind(X_6707,$fot(X_6708))]]) ).
cnf(refute_0_43,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_52,tc_set(t_a)),v_n,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x,X_6708,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_52,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_6708,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) )],[refute_0_42,refute_0_13]) ).
cnf(refute_0_44,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_43:[bind(X_52,$fot(v_n)),bind(X_6708,$fot(v_n))]]) ).
cnf(refute_0_45,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a)) )],[refute_0_44,refute_0_3]) ).
cnf(refute_0_46,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) )],[refute_0_45,cls_conjecture_4]) ).
cnf(refute_0_47,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) )],[refute_0_46,refute_0_2]) ).
cnf(refute_0_48,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,v_Y,tc_set(tc_set(t_a))) )],[cls_conjecture_3,refute_0_47]) ).
cnf(refute_0_49,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_n = v_x ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_48,cls_conjecture_5]) ).
cnf(refute_0_50,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| v_x != v_x
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x) ),[0],$fot(v_x)]]) ).
cnf(refute_0_51,plain,
( v_x != v_x
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_n = v_x ),
inference(resolve,[$cnf( $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( v_x != v_x
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x) )],[refute_0_51,refute_0_21]) ).
cnf(refute_0_53,plain,
v_x = v_x,
introduced(tautology,[refl,[$fot(v_x)]]) ).
cnf(refute_0_54,plain,
( v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_x,v_x) )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
( v_n = v_x
| c_in(c_Main_OsubsetI__1(v_x,X_52,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X_52,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) )],[refute_0_54,refute_0_13]) ).
cnf(refute_0_56,plain,
( v_n = v_x
| c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_55:[bind(X_52,$fot(v_n))]]) ).
cnf(refute_0_57,plain,
( v_n = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_x,v_n,tc_set(t_a)),v_n,tc_set(t_a)) )],[refute_0_56,refute_0_3]) ).
cnf(refute_0_58,plain,
( v_n = v_x
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) )],[refute_0_57,cls_conjecture_4]) ).
cnf(refute_0_59,plain,
( ~ c_in(v_x,v_Y,tc_set(tc_set(t_a)))
| v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) )],[refute_0_58,refute_0_2]) ).
cnf(refute_0_60,plain,
( v_n = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,v_Y,tc_set(tc_set(t_a))) )],[cls_conjecture_3,refute_0_59]) ).
cnf(refute_0_61,plain,
v_n = v_x,
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_60,cls_conjecture_5]) ).
cnf(refute_0_62,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_63,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_64,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( v_n != v_x
| v_x = v_n ),
inference(subst,[],[refute_0_64:[bind(X,$fot(v_n)),bind(Y,$fot(v_x))]]) ).
cnf(refute_0_66,plain,
v_x = v_n,
inference(resolve,[$cnf( $equal(v_n,v_x) )],[refute_0_61,refute_0_65]) ).
cnf(refute_0_67,plain,
( v_x != v_n
| ~ c_lessequals(v_n,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),[0],$fot(v_n)]]) ).
cnf(refute_0_68,plain,
( ~ c_lessequals(v_n,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_x,v_n) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
~ c_lessequals(v_n,v_n,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_lessequals(v_x,v_n,tc_set(tc_set(t_a))) )],[refute_0_68,cls_conjecture_4]) ).
cnf(refute_0_70,plain,
( ~ c_in(c_Main_OsubsetI__1(X_7,X_7,X_6),X_7,X_6)
| c_lessequals(X_7,X_7,tc_set(X_6)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(X_6)),bind(V_A,$fot(X_7)),bind(V_B,$fot(X_7))]]) ).
cnf(refute_0_71,plain,
( c_in(c_Main_OsubsetI__1(X_7,X_7,X_6),X_7,X_6)
| c_lessequals(X_7,X_7,tc_set(X_6)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_6)),bind(V_A,$fot(X_7)),bind(V_B,$fot(X_7))]]) ).
cnf(refute_0_72,plain,
c_lessequals(X_7,X_7,tc_set(X_6)),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_7,X_7,X_6),X_7,X_6) )],[refute_0_71,refute_0_70]) ).
cnf(refute_0_73,plain,
c_lessequals(v_n,v_n,tc_set(tc_set(t_a))),
inference(subst,[],[refute_0_72:[bind(X_6,$fot(tc_set(t_a))),bind(X_7,$fot(v_n))]]) ).
cnf(refute_0_74,plain,
$false,
inference(resolve,[$cnf( c_lessequals(v_n,v_n,tc_set(tc_set(t_a))) )],[refute_0_73,refute_0_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET857-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 19:17:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.38/30.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.38/30.59
% 30.38/30.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.42/30.59
%------------------------------------------------------------------------------