TSTP Solution File: SET839-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET839-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 03:37:40 EDT 2022
% Result : Unsatisfiable 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of clauses : 31 ( 9 unt; 13 nHn; 16 RR)
% Number of literals : 69 ( 11 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 58 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_lessequals(V_U,V_V,tc_set(t_a))
| ~ c_in(V_V,v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,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(refute_0_0,plain,
c_in(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_set(t_a))),bind(V_B,$fot(c_emptyset)),bind(V_x,$fot(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a))))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_S)),bind(V_B,$fot(c_insert(X_31,c_emptyset,tc_set(t_a))))]]) ).
cnf(refute_0_2,plain,
( c_in(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),v_S,tc_set(t_a))
| c_lessequals(v_S,V_B,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_S))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(X_14,v_S,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),v_S,tc_set(t_a))
| c_lessequals(X_14,c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),tc_set(t_a)) ),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(X_14)),bind(V_V,$fot(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a))))]]) ).
cnf(refute_0_4,plain,
( ~ c_in(X_14,v_S,tc_set(t_a))
| c_lessequals(X_14,c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,V_B,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),v_S,tc_set(t_a)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),v_S,tc_set(t_a))
| c_lessequals(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_21,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X_21,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_4:[bind(V_B,$fot(X_21)),bind(X_14,$fot(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a))))]]) ).
cnf(refute_0_6,plain,
( c_lessequals(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_21,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,V_B,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X_21,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_S,V_B,tc_set(t_a)),v_S,tc_set(t_a)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( c_lessequals(c_Main_OsubsetI__1(v_S,X_26,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_25,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X_25,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X_26,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_6:[bind(V_B,$fot(X_26)),bind(X_21,$fot(X_25))]]) ).
cnf(refute_0_8,plain,
( ~ c_lessequals(c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a)),tc_set(t_a))
| c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a)) ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)))),bind(V_B,$fot(c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a))))]]) ).
cnf(refute_0_9,plain,
( c_lessequals(c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X_23,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X_24,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_6:[bind(V_B,$fot(X_23)),bind(X_21,$fot(X_24))]]) ).
cnf(refute_0_10,plain,
( ~ c_lessequals(c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a)),tc_set(t_a))
| c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a))
| c_lessequals(v_S,X_23,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X_24,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Main_OsubsetI__1(v_S,X_23,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_24,tc_set(t_a)),tc_set(t_a)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ c_lessequals(c_Main_OsubsetI__1(v_S,X_26,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_25,tc_set(t_a)),tc_set(t_a))
| c_Main_OsubsetI__1(v_S,X_26,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X_25,tc_set(t_a))
| c_lessequals(v_S,X_25,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X_26,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_10:[bind(X_23,$fot(X_25)),bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_12,plain,
( c_Main_OsubsetI__1(v_S,X_26,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X_25,tc_set(t_a))
| c_lessequals(v_S,X_25,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X_26,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Main_OsubsetI__1(v_S,X_26,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X_25,tc_set(t_a)),tc_set(t_a)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( c_Main_OsubsetI__1(v_S,X_28,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X_28,tc_set(tc_set(t_a)))
| c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_12:[bind(X_25,$fot(c_insert(V_U,c_emptyset,tc_set(t_a)))),bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_14,plain,
( c_Main_OsubsetI__1(v_S,X_28,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X_28,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_13,cls_conjecture_0]) ).
cnf(refute_0_15,plain,
( c_Main_OsubsetI__1(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(X_29,c_emptyset,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_14:[bind(V_U,$fot(X_29)),bind(X_28,$fot(c_insert(V_U,c_emptyset,tc_set(t_a))))]]) ).
cnf(refute_0_16,plain,
c_Main_OsubsetI__1(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(X_29,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(resolve,[$cnf( c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_15,cls_conjecture_0]) ).
cnf(refute_0_17,plain,
c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(subst,[],[refute_0_16:[bind(V_U,$fot(X_31)),bind(X_29,$fot(X_32))]]) ).
cnf(refute_0_18,plain,
( c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)) != c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
introduced(tautology,[equality,[$cnf( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),[0],$fot(c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a)))]]) ).
cnf(refute_0_19,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(resolve,[$cnf( $equal(c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)) )],[refute_0_19,refute_0_1]) ).
cnf(refute_0_21,plain,
~ c_lessequals(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(X_31))]]) ).
cnf(refute_0_22,plain,
~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_32,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(resolve,[$cnf( c_lessequals(v_S,c_insert(X_31,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(subst,[],[refute_0_22:[bind(X_31,$fot(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a)))),bind(X_32,$fot(X_35))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(c_Main_OsubsetI__1(v_S,c_insert(X_35,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_emptyset,tc_set(t_a)),tc_set(t_a)) )],[refute_0_0,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET839-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.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 14:14:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------