TSTP Solution File: SET843-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 03:37:42 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of clauses : 66 ( 22 unt; 4 nHn; 61 RR)
% Number of literals : 129 ( 66 equ; 63 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OUnion__upper_0,axiom,
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| V_A = V_B ) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(V_A,V_A,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_OsuccI_0,axiom,
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__UnionI_0,axiom,
( ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))
| c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_Oeq__succ__upper_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)))
| V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a))) ) ).
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,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ) ).
cnf(refute_0_0,plain,
c_lessequals(c_Zorn_OTFin(X_15,X_14),c_Zorn_OTFin(X_15,X_14),tc_set(tc_set(tc_set(X_14)))),
inference(subst,[],[cls_Set_Osubset__refl_0:[bind(T_a,$fot(tc_set(tc_set(X_14)))),bind(V_A,$fot(c_Zorn_OTFin(X_15,X_14)))]]) ).
cnf(refute_0_1,plain,
( ~ c_lessequals(c_Zorn_OTFin(X_15,X_14),c_Zorn_OTFin(X_15,X_14),tc_set(tc_set(tc_set(X_14))))
| c_in(c_Union(c_Zorn_OTFin(X_15,X_14),tc_set(X_14)),c_Zorn_OTFin(X_15,X_14),tc_set(tc_set(X_14))) ),
inference(subst,[],[cls_Zorn_OTFin__UnionI_0:[bind(T_a,$fot(X_14)),bind(V_S,$fot(X_15)),bind(V_Y,$fot(c_Zorn_OTFin(X_15,X_14)))]]) ).
cnf(refute_0_2,plain,
c_in(c_Union(c_Zorn_OTFin(X_15,X_14),tc_set(X_14)),c_Zorn_OTFin(X_15,X_14),tc_set(tc_set(X_14))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_OTFin(X_15,X_14),c_Zorn_OTFin(X_15,X_14),tc_set(tc_set(tc_set(X_14)))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(subst,[],[refute_0_2:[bind(X_14,$fot(t_a)),bind(X_15,$fot(v_S))]]) ).
cnf(refute_0_4,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_in(X_28,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_28,v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_Oeq__succ__upper_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(v_m)),bind(V_n,$fot(X_28))]]) ).
cnf(refute_0_5,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_in(X_28,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_28,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Set_OUnion__upper_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Zorn_OTFin(v_S,t_a))),bind(V_B,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).
cnf(refute_0_7,plain,
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin_OsuccI_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_x,$fot(v_m))]]) ).
cnf(refute_0_8,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_7]) ).
cnf(refute_0_9,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m ),
inference(subst,[],[refute_0_12:[bind(X,$fot(v_m)),bind(Y,$fot(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))))]]) ).
cnf(refute_0_14,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolve,[$cnf( $equal(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) )],[cls_conjecture_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),[1],$fot(v_m)]]) ).
cnf(refute_0_16,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_m)),bind(V_B,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).
cnf(refute_0_19,plain,
( ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(subst,[],[cls_Zorn_OAbrial__axiom1_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_x,$fot(v_m))]]) ).
cnf(refute_0_21,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(resolve,[$cnf( c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(subst,[],[refute_0_12:[bind(X,$fot(v_m)),bind(Y,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).
cnf(refute_0_23,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(resolve,[$cnf( $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| v_m != v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) ),[1],$fot(v_m)]]) ).
cnf(refute_0_25,plain,
( v_m != v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( v_m != v_m
| ~ c_in(X_28,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_28,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) )],[refute_0_25,refute_0_5]) ).
cnf(refute_0_27,plain,
v_m = v_m,
introduced(tautology,[refl,[$fot(v_m)]]) ).
cnf(refute_0_28,plain,
( ~ c_in(X_28,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_28,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_m,v_m) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_28:[bind(X_28,$fot(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))))]]) ).
cnf(refute_0_30,plain,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_3,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ c_in(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Set_OUnion__upper_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Zorn_OTFin(v_S,t_a))),bind(V_B,$fot(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a)))]]) ).
cnf(refute_0_32,plain,
( ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin_OsuccI_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_x,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).
cnf(refute_0_33,plain,
c_in(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_8,refute_0_32]) ).
cnf(refute_0_34,plain,
c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_33,refute_0_31]) ).
cnf(refute_0_35,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a))),bind(V_B,$fot(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))))]]) ).
cnf(refute_0_36,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),
introduced(tautology,[refl,[$fot(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a))]]) ).
cnf(refute_0_38,plain,
( c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) != c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a)
| c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a)) ),[1,1],$fot(v_m)]]) ).
cnf(refute_0_39,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = c_Zorn_Osucc(v_S,v_m,t_a),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) )],[refute_0_23,refute_0_39]) ).
cnf(refute_0_41,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_42,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_12,refute_0_41]) ).
cnf(refute_0_43,plain,
( c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) != c_Zorn_Osucc(v_S,v_m,t_a)
| c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = v_m ),
inference(subst,[],[refute_0_42:[bind(X,$fot(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a))),bind(Y,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(Z,$fot(v_m))]]) ).
cnf(refute_0_44,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = v_m ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Zorn_Osucc(v_S,v_m,t_a)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = v_m,
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) )],[refute_0_23,refute_0_44]) ).
cnf(refute_0_46,plain,
( c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) != v_m
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),tc_set(tc_set(t_a))) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),tc_set(tc_set(t_a))) ),[1],$fot(v_m)]]) ).
cnf(refute_0_47,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),v_m) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(resolve,[$cnf( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),tc_set(tc_set(t_a))) )],[refute_0_47,refute_0_36]) ).
cnf(refute_0_49,plain,
( c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) != v_m
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) ),[0],$fot(v_m)]]) ).
cnf(refute_0_50,plain,
( c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),v_m) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,v_m,t_a),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m != v_m ),
inference(resolve,[$cnf( $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) )],[refute_0_25,cls_conjecture_1]) ).
cnf(refute_0_53,plain,
v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(resolve,[$cnf( $equal(v_m,v_m) )],[refute_0_27,refute_0_52]) ).
cnf(refute_0_54,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( $equal(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_30,refute_0_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n019.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 04:33:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------