TSTP Solution File: SET858-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 03:37:54 EDT 2022
% Result : Unsatisfiable 0.85s 1.01s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of clauses : 52 ( 12 unt; 32 nHn; 50 RR)
% Number of literals : 157 ( 26 equ; 57 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),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_2,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ).
cnf(cls_Set_Osubset__trans_0,axiom,
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_lessequals(V_A,V_C,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_Zorn_OTFin__linear__lemma2_0,axiom,
( ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| V_U = V_m ) ).
cnf(refute_0_0,plain,
c_lessequals(X_4,c_Zorn_Osucc(V_S,X_4,T_a),tc_set(tc_set(T_a))),
inference(subst,[],[cls_Zorn_OAbrial__axiom1_0:[bind(V_x,$fot(X_4))]]) ).
cnf(refute_0_1,plain,
( ~ c_lessequals(X_4,c_Zorn_Osucc(V_S,X_4,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,X_4,T_a),X_6,tc_set(tc_set(T_a)))
| c_lessequals(X_4,X_6,tc_set(tc_set(T_a))) ),
inference(subst,[],[cls_Set_Osubset__trans_0:[bind(T_a,$fot(tc_set(T_a))),bind(V_A,$fot(X_4)),bind(V_B,$fot(c_Zorn_Osucc(V_S,X_4,T_a))),bind(V_C,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( ~ c_lessequals(c_Zorn_Osucc(V_S,X_4,T_a),X_6,tc_set(tc_set(T_a)))
| c_lessequals(X_4,X_6,tc_set(tc_set(T_a))) ),
inference(resolve,[$cnf( c_lessequals(X_4,c_Zorn_Osucc(V_S,X_4,T_a),tc_set(tc_set(T_a))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_2:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(X_4,$fot(v_m)),bind(X_6,$fot(v_n))]]) ).
cnf(refute_0_4,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m
| ~ c_in(X_204,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_204,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X_204,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,$fot(v_m)),bind(V_n,$fot(X_204))]]) ).
cnf(refute_0_5,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m
| ~ c_in(X_204,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_204,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X_204,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_4]) ).
cnf(refute_0_6,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_5:[bind(X_204,$fot(v_n))]]) ).
cnf(refute_0_7,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) )],[refute_0_7,cls_conjecture_2]) ).
cnf(refute_0_9,plain,
( ~ c_in(X_178,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X_178,v_m,tc_set(tc_set(t_a)))
| X_178 = v_m
| c_lessequals(c_Zorn_Osucc(v_S,X_178,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma2_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_U,$fot(X_178)),bind(V_m,$fot(v_m))]]) ).
cnf(refute_0_10,plain,
( ~ c_in(X_178,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X_178,v_m,tc_set(tc_set(t_a)))
| X_178 = v_m
| c_lessequals(c_Zorn_Osucc(v_S,X_178,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_10:[bind(X_178,$fot(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a)))]]) ).
cnf(refute_0_12,plain,
( ~ c_in(X_417,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,X_417,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_417,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X_417,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,$fot(X_417)),bind(V_n,$fot(v_n))]]) ).
cnf(refute_0_13,plain,
( ~ c_in(X_417,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X_417,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_417,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X_417,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_13:[bind(X_417,$fot(v_m))]]) ).
cnf(refute_0_15,plain,
( 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(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_14]) ).
cnf(refute_0_16,plain,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) )],[refute_0_15,cls_conjecture_2]) ).
cnf(refute_0_17,plain,
( ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m
| 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(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_16,refute_0_11]) ).
cnf(refute_0_18,plain,
( ~ c_in(X_236,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_236,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X_236,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_1:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(v_m)),bind(V_n,$fot(X_236))]]) ).
cnf(refute_0_19,plain,
( ~ c_in(X_236,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_236,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X_236,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ 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,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)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_19:[bind(X_236,$fot(v_n))]]) ).
cnf(refute_0_21,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_20]) ).
cnf(refute_0_22,plain,
( 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))) ),
inference(resolve,[$cnf( c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) )],[refute_0_21,cls_conjecture_2]) ).
cnf(refute_0_23,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) )],[refute_0_22,refute_0_3]) ).
cnf(refute_0_24,plain,
c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) )],[refute_0_23,cls_conjecture_3]) ).
cnf(refute_0_25,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) )],[refute_0_24,refute_0_17]) ).
cnf(refute_0_26,plain,
( ~ c_in(X_459,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,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(X_459,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X_459,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,$fot(v_m)),bind(V_n,$fot(X_459))]]) ).
cnf(refute_0_27,plain,
( ~ c_in(X_459,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,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(X_459,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X_459,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))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ c_in(X_459,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m
| c_lessequals(X_459,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X_459,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_27]) ).
cnf(refute_0_29,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_m,t_a) = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_28:[bind(X_459,$fot(v_n))]]) ).
cnf(refute_0_30,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_29]) ).
cnf(refute_0_31,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) )],[refute_0_30,cls_conjecture_2]) ).
cnf(refute_0_32,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) )],[refute_0_31,refute_0_3]) ).
cnf(refute_0_33,plain,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m,
inference(resolve,[$cnf( c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) )],[refute_0_32,cls_conjecture_3]) ).
cnf(refute_0_34,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m
| v_m != v_m
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m) ),[0],$fot(v_m)]]) ).
cnf(refute_0_35,plain,
( v_m != v_m
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m ),
inference(resolve,[$cnf( $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( v_m != v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m) )],[refute_0_35,refute_0_8]) ).
cnf(refute_0_37,plain,
v_m = v_m,
introduced(tautology,[refl,[$fot(v_m)]]) ).
cnf(refute_0_38,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( $equal(v_m,v_m) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) )],[refute_0_38,refute_0_3]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) )],[refute_0_39,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n016.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 : Mon Jul 11 01:22:57 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.85/1.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.85/1.01
% 0.85/1.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.85/1.01
%------------------------------------------------------------------------------