TSTP Solution File: SET820-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET820-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 03:37:26 EDT 2022
% Result : Unsatisfiable 0.09s 0.32s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 15 unt; 4 nHn; 16 RR)
% Number of literals : 38 ( 7 equ; 17 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 : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 39 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OemptyE_0,axiom,
~ c_in(V_a,c_emptyset,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_OinsertE_0,axiom,
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| V_a = V_b ) ).
cnf(cls_conjecture_0,negated_conjecture,
v_P(v_a) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(V_V,V_U,tc_IntDef_Oint)
| c_in(v_x(V_U),V_U,tc_IntDef_Oint) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ c_in(V_W,V_U,tc_IntDef_Oint)
| ~ v_P(v_x(V_U)) ) ).
cnf(refute_0_0,plain,
c_in(X_6,c_insert(X_6,V_B,tc_IntDef_Oint),tc_IntDef_Oint),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_x,$fot(X_6))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(X_6,c_insert(X_6,V_B,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ v_P(v_x(c_insert(X_6,V_B,tc_IntDef_Oint))) ),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(c_insert(X_6,V_B,tc_IntDef_Oint))),bind(V_W,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
~ v_P(v_x(c_insert(X_6,V_B,tc_IntDef_Oint))),
inference(resolve,[$cnf( c_in(X_6,c_insert(X_6,V_B,tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
~ v_P(v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint))),
inference(subst,[],[refute_0_2:[bind(V_B,$fot(c_emptyset))]]) ).
cnf(refute_0_4,plain,
~ c_in(v_x(c_insert(X_18,c_emptyset,tc_IntDef_Oint)),c_emptyset,tc_IntDef_Oint),
inference(subst,[],[cls_Set_OemptyE_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_a,$fot(v_x(c_insert(X_18,c_emptyset,tc_IntDef_Oint))))]]) ).
cnf(refute_0_5,plain,
c_in(X_10,c_insert(X_10,V_B,tc_IntDef_Oint),tc_IntDef_Oint),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_x,$fot(X_10))]]) ).
cnf(refute_0_6,plain,
( ~ c_in(X_10,c_insert(X_10,V_B,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_x(c_insert(X_10,V_B,tc_IntDef_Oint)),c_insert(X_10,V_B,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(c_insert(X_10,V_B,tc_IntDef_Oint))),bind(V_V,$fot(X_10))]]) ).
cnf(refute_0_7,plain,
c_in(v_x(c_insert(X_10,V_B,tc_IntDef_Oint)),c_insert(X_10,V_B,tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolve,[$cnf( c_in(X_10,c_insert(X_10,V_B,tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
c_in(v_x(c_insert(X_16,X_14,tc_IntDef_Oint)),c_insert(X_16,X_14,tc_IntDef_Oint),tc_IntDef_Oint),
inference(subst,[],[refute_0_7:[bind(V_B,$fot(X_14)),bind(X_10,$fot(X_16))]]) ).
cnf(refute_0_9,plain,
( ~ c_in(v_x(c_insert(X_16,X_14,tc_IntDef_Oint)),c_insert(X_16,X_14,tc_IntDef_Oint),tc_IntDef_Oint)
| v_x(c_insert(X_16,X_14,tc_IntDef_Oint)) = X_16
| c_in(v_x(c_insert(X_16,X_14,tc_IntDef_Oint)),X_14,tc_IntDef_Oint) ),
inference(subst,[],[cls_Set_OinsertE_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_A,$fot(X_14)),bind(V_a,$fot(v_x(c_insert(X_16,X_14,tc_IntDef_Oint)))),bind(V_b,$fot(X_16))]]) ).
cnf(refute_0_10,plain,
( v_x(c_insert(X_16,X_14,tc_IntDef_Oint)) = X_16
| c_in(v_x(c_insert(X_16,X_14,tc_IntDef_Oint)),X_14,tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_in(v_x(c_insert(X_16,X_14,tc_IntDef_Oint)),c_insert(X_16,X_14,tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( v_x(c_insert(X_18,c_emptyset,tc_IntDef_Oint)) = X_18
| c_in(v_x(c_insert(X_18,c_emptyset,tc_IntDef_Oint)),c_emptyset,tc_IntDef_Oint) ),
inference(subst,[],[refute_0_10:[bind(X_14,$fot(c_emptyset)),bind(X_16,$fot(X_18))]]) ).
cnf(refute_0_12,plain,
v_x(c_insert(X_18,c_emptyset,tc_IntDef_Oint)) = X_18,
inference(resolve,[$cnf( c_in(v_x(c_insert(X_18,c_emptyset,tc_IntDef_Oint)),c_emptyset,tc_IntDef_Oint) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint)) = X_6,
inference(subst,[],[refute_0_12:[bind(X_18,$fot(X_6))]]) ).
cnf(refute_0_14,plain,
( v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint)) != X_6
| ~ v_P(X_6)
| v_P(v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint))) ),
introduced(tautology,[equality,[$cnf( ~ v_P(v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint))) ),[0],$fot(X_6)]]) ).
cnf(refute_0_15,plain,
( ~ v_P(X_6)
| v_P(v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint))) ),
inference(resolve,[$cnf( $equal(v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint)),X_6) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
~ v_P(X_6),
inference(resolve,[$cnf( v_P(v_x(c_insert(X_6,c_emptyset,tc_IntDef_Oint))) )],[refute_0_15,refute_0_3]) ).
cnf(refute_0_17,plain,
~ v_P(v_a),
inference(subst,[],[refute_0_16:[bind(X_6,$fot(v_a))]]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( v_P(v_a) )],[cls_conjecture_0,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET820-2 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.31 % Computer : n013.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 600
% 0.09/0.31 % DateTime : Sat Jul 9 18:45:59 EDT 2022
% 0.09/0.31 % CPUTime :
% 0.09/0.31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.32
% 0.09/0.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.09/0.32
%------------------------------------------------------------------------------