TSTP Solution File: SET852-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET852-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 03:37:49 EDT 2022
% Result : Unsatisfiable 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 4 unt; 14 nHn; 12 RR)
% Number of literals : 45 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,v_Y,tc_set(tc_set(t_a))) ) ).
cnf(cls_Zorn_OUnion__lemma0_0,axiom,
( c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).
cnf(cls_Zorn_OUnion__lemma0_1,axiom,
( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).
cnf(cls_Zorn_OUnion__lemma0_2,axiom,
( ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a)) ) ).
cnf(refute_0_0,plain,
( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OUnion__lemma0_1:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_m)),bind(V_B,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(V_C,$fot(v_Y))]]) ).
cnf(refute_0_1,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OUnion__lemma0_2:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(X_13)),bind(V_B,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(V_C,$fot(v_Y))]]) ).
cnf(refute_0_2,plain,
( ~ c_in(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_conjecture_4:[bind(V_U,$fot(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a))))]]) ).
cnf(refute_0_3,plain,
( c_in(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X_3,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_2,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OUnion__lemma0_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(X_2)),bind(V_B,$fot(X_3)),bind(V_C,$fot(v_Y))]]) ).
cnf(refute_0_4,plain,
( c_lessequals(X_3,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_2,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Zorn_OUnion__lemma0__1(X_2,X_3,v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_4:[bind(X_2,$fot(X_13)),bind(X_3,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).
cnf(refute_0_6,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X_13,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X_13,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_6,cls_conjecture_3]) ).
cnf(refute_0_8,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_7:[bind(X_13,$fot(v_m))]]) ).
cnf(refute_0_9,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_9,cls_conjecture_2]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_10,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET852-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 05:23:57 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35
% 0.14/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36
%------------------------------------------------------------------------------