TSTP Solution File: SET842-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET842-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:37:42 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 3 unt; 12 nHn; 16 RR)
% Number of literals : 51 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_4,negated_conjecture,
( 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_Set_OUnionE_0,axiom,
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUnionE_1,axiom,
( ~ c_in(V_A,c_Union(V_C,T_a),T_a)
| c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a) ) ).
cnf(cls_Set_OsubsetD_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,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(refute_0_0,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Union(v_Y,tc_set(t_a)))),bind(V_B,$fot(v_m))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Union(V_C,X_4),X_4)
| c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),V_C,X_4),X_4) ),
inference(subst,[],[cls_Set_OUnionE_1:[bind(T_a,$fot(X_4)),bind(V_A,$fot(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4)))]]) ).
cnf(refute_0_2,plain,
( c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Union(V_C,X_4),X_4)
| c_lessequals(c_Union(V_C,X_4),X_6,tc_set(X_4)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_4)),bind(V_A,$fot(c_Union(V_C,X_4))),bind(V_B,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
( c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),V_C,X_4),X_4)
| c_lessequals(c_Union(V_C,X_4),X_6,tc_set(X_4)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(V_C,X_4),X_6,X_4),c_Union(V_C,X_4),X_4) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_3:[bind(V_C,$fot(v_Y)),bind(X_4,$fot(tc_set(t_a))),bind(X_6,$fot(X_40))]]) ).
cnf(refute_0_5,plain,
( ~ c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_conjecture_4:[bind(V_U,$fot(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a))))]]) ).
cnf(refute_0_6,plain,
( c_in(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),c_Union(X_15,X_13),X_13)
| c_lessequals(c_Union(X_15,X_13),V_B,tc_set(X_13)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_13)),bind(V_A,$fot(c_Union(X_15,X_13)))]]) ).
cnf(refute_0_7,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),c_Union(X_15,X_13),X_13)
| c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),X_15,X_13),X_15,tc_set(X_13)) ),
inference(subst,[],[cls_Set_OUnionE_0:[bind(T_a,$fot(X_13)),bind(V_A,$fot(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13))),bind(V_C,$fot(X_15))]]) ).
cnf(refute_0_8,plain,
( c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),X_15,X_13),X_15,tc_set(X_13))
| c_lessequals(c_Union(X_15,X_13),V_B,tc_set(X_13)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(X_15,X_13),V_B,X_13),c_Union(X_15,X_13),X_13) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_8:[bind(V_B,$fot(X_16)),bind(X_13,$fot(tc_set(t_a))),bind(X_15,$fot(v_Y))]]) ).
cnf(refute_0_10,plain,
( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(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)),X_16,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
( ~ c_in(X_23,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_in(X_23,v_m,tc_set(t_a)) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)))),bind(V_B,$fot(v_m)),bind(V_c,$fot(X_23))]]) ).
cnf(refute_0_12,plain,
( ~ c_in(X_23,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(X_23,v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_16,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_12:[bind(X_16,$fot(X_40)),bind(X_23,$fot(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a))))]]) ).
cnf(refute_0_14,plain,
( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X_40,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a)) )],[refute_0_4,refute_0_13]) ).
cnf(refute_0_15,plain,
( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_14:[bind(X_40,$fot(v_m))]]) ).
cnf(refute_0_16,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(t_a)),v_m,tc_set(t_a)) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) )],[refute_0_16,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET842-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.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 05:34:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------