TSTP Solution File: SET844-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET844-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 03:37:43 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 12 unt; 0 nHn; 21 RR)
% Number of literals : 46 ( 20 equ; 22 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 : 24 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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_Zorn_Osucc(v_S,v_m,t_a) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).
cnf(refute_0_0,plain,
c_lessequals(c_Zorn_OTFin(X_3,X_2),c_Zorn_OTFin(X_3,X_2),tc_set(tc_set(tc_set(X_2)))),
inference(subst,[],[cls_Set_Osubset__refl_0:[bind(T_a,$fot(tc_set(tc_set(X_2)))),bind(V_A,$fot(c_Zorn_OTFin(X_3,X_2)))]]) ).
cnf(refute_0_1,plain,
( ~ c_lessequals(c_Zorn_OTFin(X_3,X_2),c_Zorn_OTFin(X_3,X_2),tc_set(tc_set(tc_set(X_2))))
| c_in(c_Union(c_Zorn_OTFin(X_3,X_2),tc_set(X_2)),c_Zorn_OTFin(X_3,X_2),tc_set(tc_set(X_2))) ),
inference(subst,[],[cls_Zorn_OTFin__UnionI_0:[bind(T_a,$fot(X_2)),bind(V_S,$fot(X_3)),bind(V_Y,$fot(c_Zorn_OTFin(X_3,X_2)))]]) ).
cnf(refute_0_2,plain,
c_in(c_Union(c_Zorn_OTFin(X_3,X_2),tc_set(X_2)),c_Zorn_OTFin(X_3,X_2),tc_set(tc_set(X_2))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_OTFin(X_3,X_2),c_Zorn_OTFin(X_3,X_2),tc_set(tc_set(tc_set(X_2)))) )],[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_2,$fot(t_a)),bind(X_3,$fot(v_S))]]) ).
cnf(refute_0_4,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_in(X_10,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_10,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_10))]]) ).
cnf(refute_0_5,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_in(X_10,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_10,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_4]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(subst,[],[refute_0_8:[bind(X,$fot(v_m)),bind(Y,$fot(c_Zorn_Osucc(v_S,v_m,t_a)))]]) ).
cnf(refute_0_10,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(resolve,[$cnf( $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) )],[cls_conjecture_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != v_m
| v_m != v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) ),[1],$fot(v_m)]]) ).
cnf(refute_0_12,plain,
( v_m != v_m
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_m,t_a),v_m) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( v_m != v_m
| ~ c_in(X_10,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_10,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_m,c_Zorn_Osucc(v_S,v_m,t_a)) )],[refute_0_12,refute_0_5]) ).
cnf(refute_0_14,plain,
v_m = v_m,
introduced(tautology,[refl,[$fot(v_m)]]) ).
cnf(refute_0_15,plain,
( ~ c_in(X_10,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_10,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_m,v_m) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_15:[bind(X_10,$fot(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))))]]) ).
cnf(refute_0_17,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_16]) ).
cnf(refute_0_18,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_17,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET844-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n004.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 23:05:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------