TSTP Solution File: SET845-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:37:44 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 13 unt; 0 nHn; 24 RR)
% Number of literals : 43 ( 19 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 17 ( 1 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_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_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)) ).
cnf(cls_conjecture_2,negated_conjecture,
v_m != c_Zorn_Osucc(v_S,v_m,t_a) ).
cnf(refute_0_0,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,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin_OsuccI_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_x,$fot(v_m))]]) ).
cnf(refute_0_2,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,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_1]) ).
cnf(refute_0_3,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolve,[$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_2,refute_0_0]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m ),
inference(subst,[],[refute_0_6:[bind(X,$fot(v_m)),bind(Y,$fot(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))))]]) ).
cnf(refute_0_8,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(resolve,[$cnf( $equal(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))) )],[cls_conjecture_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) ),
introduced(tautology,[equality,[$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],$fot(v_m)]]) ).
cnf(refute_0_10,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(resolve,[$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_3,refute_0_10]) ).
cnf(refute_0_12,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)))
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(V_B,$fot(v_m))]]) ).
cnf(refute_0_13,plain,
( ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,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,$fot(v_m))]]) ).
cnf(refute_0_15,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(resolve,[$cnf( c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(Y,$fot(v_m))]]) ).
cnf(refute_0_17,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_16,cls_conjecture_2]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) )],[refute_0_15,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 08:26:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------