%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET848-2 : 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 03:37:46 EDT 2022
% Result : Unsatisfiable 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 10 unt; 4 nHn; 16 RR)
% Number of literals : 43 ( 12 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 39 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_ODiffI_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(V_A,V_A,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_OTFin__chain__lemma4_0,axiom,
( ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_Osucc__not__equals_0,axiom,
( ~ c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a)))
| c_Zorn_Osucc(V_S,V_c,T_a) != V_c ) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ).
cnf(refute_0_0,plain,
( c_Zorn_Osucc(X_21,c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20)),X_20) != c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20))
| ~ c_in(c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20)),c_minus(c_Zorn_Ochain(X_21,X_20),c_Zorn_Omaxchain(X_21,X_20),tc_set(tc_set(tc_set(X_20)))),tc_set(tc_set(X_20))) ),
inference(subst,[],[cls_Zorn_Osucc__not__equals_0:[bind(T_a,$fot(X_20)),bind(V_S,$fot(X_21)),bind(V_c,$fot(c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20))))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_Zorn_OTFin(X_9,X_8),tc_set(tc_set(X_8)))
| c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_Zorn_Ochain(X_9,X_8),tc_set(tc_set(X_8))) ),
inference(subst,[],[cls_Zorn_OTFin__chain__lemma4_0:[bind(T_a,$fot(X_8)),bind(V_S,$fot(X_9)),bind(V_c,$fot(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8))))]]) ).
cnf(refute_0_2,plain,
c_lessequals(c_Zorn_OTFin(X_6,X_5),c_Zorn_OTFin(X_6,X_5),tc_set(tc_set(tc_set(X_5)))),
inference(subst,[],[cls_Set_Osubset__refl_0:[bind(T_a,$fot(tc_set(tc_set(X_5)))),bind(V_A,$fot(c_Zorn_OTFin(X_6,X_5)))]]) ).
cnf(refute_0_3,plain,
( ~ c_lessequals(c_Zorn_OTFin(X_6,X_5),c_Zorn_OTFin(X_6,X_5),tc_set(tc_set(tc_set(X_5))))
| c_in(c_Union(c_Zorn_OTFin(X_6,X_5),tc_set(X_5)),c_Zorn_OTFin(X_6,X_5),tc_set(tc_set(X_5))) ),
inference(subst,[],[cls_Zorn_OTFin__UnionI_0:[bind(T_a,$fot(X_5)),bind(V_S,$fot(X_6)),bind(V_Y,$fot(c_Zorn_OTFin(X_6,X_5)))]]) ).
cnf(refute_0_4,plain,
c_in(c_Union(c_Zorn_OTFin(X_6,X_5),tc_set(X_5)),c_Zorn_OTFin(X_6,X_5),tc_set(tc_set(X_5))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_OTFin(X_6,X_5),c_Zorn_OTFin(X_6,X_5),tc_set(tc_set(tc_set(X_5)))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_Zorn_OTFin(X_9,X_8),tc_set(tc_set(X_8))),
inference(subst,[],[refute_0_4:[bind(X_5,$fot(X_8)),bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_6,plain,
c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_Zorn_Ochain(X_9,X_8),tc_set(tc_set(X_8))),
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_Zorn_OTFin(X_9,X_8),tc_set(tc_set(X_8))) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_Zorn_Ochain(X_9,X_8),tc_set(tc_set(X_8)))
| c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),X_17,tc_set(tc_set(X_8)))
| c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_minus(c_Zorn_Ochain(X_9,X_8),X_17,tc_set(tc_set(tc_set(X_8)))),tc_set(tc_set(X_8))) ),
inference(subst,[],[cls_Set_ODiffI_0:[bind(T_a,$fot(tc_set(tc_set(X_8)))),bind(V_A,$fot(c_Zorn_Ochain(X_9,X_8))),bind(V_B,$fot(X_17)),bind(V_c,$fot(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8))))]]) ).
cnf(refute_0_8,plain,
( c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),X_17,tc_set(tc_set(X_8)))
| c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_minus(c_Zorn_Ochain(X_9,X_8),X_17,tc_set(tc_set(tc_set(X_8)))),tc_set(tc_set(X_8))) ),
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OTFin(X_9,X_8),tc_set(X_8)),c_Zorn_Ochain(X_9,X_8),tc_set(tc_set(X_8))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_in(c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20)),c_Zorn_Omaxchain(X_21,X_20),tc_set(tc_set(X_20)))
| c_in(c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20)),c_minus(c_Zorn_Ochain(X_21,X_20),c_Zorn_Omaxchain(X_21,X_20),tc_set(tc_set(tc_set(X_20)))),tc_set(tc_set(X_20))) ),
inference(subst,[],[refute_0_8:[bind(X_17,$fot(c_Zorn_Omaxchain(X_21,X_20))),bind(X_8,$fot(X_20)),bind(X_9,$fot(X_21))]]) ).
cnf(refute_0_10,plain,
( c_Zorn_Osucc(X_21,c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20)),X_20) != c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20))
| c_in(c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20)),c_Zorn_Omaxchain(X_21,X_20),tc_set(tc_set(X_20))) ),
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OTFin(X_21,X_20),tc_set(X_20)),c_minus(c_Zorn_Ochain(X_21,X_20),c_Zorn_Omaxchain(X_21,X_20),tc_set(tc_set(tc_set(X_20)))),tc_set(tc_set(X_20))) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
( c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_10:[bind(X_20,$fot(t_a)),bind(X_21,$fot(v_S))]]) ).
cnf(refute_0_12,plain,
( 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))
| c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) ),[0,1],$fot(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)))]]) ).
cnf(refute_0_13,plain,
( 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))
| c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) )],[cls_conjecture_1,refute_0_12]) ).
cnf(refute_0_14,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) )],[refute_0_13,refute_0_11]) ).
cnf(refute_0_15,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
introduced(tautology,[refl,[$fot(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)))]]) ).
cnf(refute_0_16,plain,
c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( $equal(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))) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_16,cls_conjecture_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET848-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 600
% 0.20/0.34 % DateTime : Sun Jul 10 07:16:26 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.36
% 0.20/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.36
%------------------------------------------------------------------------------