TSTP Solution File: SET821-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET821-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 03:37:27 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of clauses : 59 ( 17 unt; 23 nHn; 36 RR)
% Number of literals : 118 ( 31 equ; 40 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 79 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Orderings_Oorder__less__irrefl__iff1_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_x,T_a) ) ).
cnf(cls_Set_OComplD__dest_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a) ) ).
cnf(cls_Set_OComplI_0,axiom,
( c_in(V_c,V_A,T_a)
| c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a) ) ).
cnf(cls_Set_OinsertCI_0,axiom,
( ~ c_in(V_a,V_B,T_a)
| c_in(V_a,c_insert(V_b,V_B,T_a),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,
c_less(v_a,v_b,tc_IntDef_Oint) ).
cnf(cls_conjecture_1,negated_conjecture,
c_less(v_b,v_c,tc_IntDef_Oint) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_in(v_c,V_U,tc_IntDef_Oint)
| ~ c_in(v_b,V_U,tc_IntDef_Oint)
| c_in(v_a,V_U,tc_IntDef_Oint) ) ).
cnf(clsarity_IntDef__Oint_31,axiom,
class_Orderings_Oorder(tc_IntDef_Oint) ).
cnf(refute_0_0,plain,
( ~ c_less(v_a,v_a,tc_IntDef_Oint)
| ~ class_Orderings_Oorder(tc_IntDef_Oint) ),
inference(subst,[],[cls_Orderings_Oorder__less__irrefl__iff1_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_x,$fot(v_a))]]) ).
cnf(refute_0_1,plain,
( ~ c_less(v_b,v_b,tc_IntDef_Oint)
| ~ class_Orderings_Oorder(tc_IntDef_Oint) ),
inference(subst,[],[cls_Orderings_Oorder__less__irrefl__iff1_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_x,$fot(v_b))]]) ).
cnf(refute_0_2,plain,
( ~ c_in(X_23,c_insert(X_24,c_insert(X_23,X_21,X_22),X_22),X_22)
| c_in(X_23,c_insert(V_b,c_insert(X_24,c_insert(X_23,X_21,X_22),X_22),X_22),X_22) ),
inference(subst,[],[cls_Set_OinsertCI_0:[bind(T_a,$fot(X_22)),bind(V_B,$fot(c_insert(X_24,c_insert(X_23,X_21,X_22),X_22))),bind(V_a,$fot(X_23))]]) ).
cnf(refute_0_3,plain,
c_in(X_19,c_insert(X_19,V_B,X_17),X_17),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(X_17)),bind(V_x,$fot(X_19))]]) ).
cnf(refute_0_4,plain,
( ~ c_in(X_19,c_insert(X_19,V_B,X_17),X_17)
| c_in(X_19,c_insert(X_20,c_insert(X_19,V_B,X_17),X_17),X_17) ),
inference(subst,[],[cls_Set_OinsertCI_0:[bind(T_a,$fot(X_17)),bind(V_B,$fot(c_insert(X_19,V_B,X_17))),bind(V_a,$fot(X_19)),bind(V_b,$fot(X_20))]]) ).
cnf(refute_0_5,plain,
c_in(X_19,c_insert(X_20,c_insert(X_19,V_B,X_17),X_17),X_17),
inference(resolve,[$cnf( c_in(X_19,c_insert(X_19,V_B,X_17),X_17) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
c_in(X_23,c_insert(X_24,c_insert(X_23,X_21,X_22),X_22),X_22),
inference(subst,[],[refute_0_5:[bind(V_B,$fot(X_21)),bind(X_17,$fot(X_22)),bind(X_19,$fot(X_23)),bind(X_20,$fot(X_24))]]) ).
cnf(refute_0_7,plain,
c_in(X_23,c_insert(V_b,c_insert(X_24,c_insert(X_23,X_21,X_22),X_22),X_22),X_22),
inference(resolve,[$cnf( c_in(X_23,c_insert(X_24,c_insert(X_23,X_21,X_22),X_22),X_22) )],[refute_0_6,refute_0_2]) ).
cnf(refute_0_8,plain,
c_in(v_b,c_insert(V_b,c_insert(X_24,c_insert(v_b,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),
inference(subst,[],[refute_0_7:[bind(X_22,$fot(tc_IntDef_Oint)),bind(X_23,$fot(v_b))]]) ).
cnf(refute_0_9,plain,
( ~ c_in(v_b,V_A,tc_IntDef_Oint)
| ~ c_in(v_b,c_uminus(V_A,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(subst,[],[cls_Set_OComplD__dest_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_c,$fot(v_b))]]) ).
cnf(refute_0_10,plain,
( ~ c_in(v_b,c_insert(v_a,X_62,tc_IntDef_Oint),tc_IntDef_Oint)
| v_b = v_a
| c_in(v_b,X_62,tc_IntDef_Oint) ),
inference(subst,[],[cls_Set_OinsertE_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_A,$fot(X_62)),bind(V_a,$fot(v_b)),bind(V_b,$fot(v_a))]]) ).
cnf(refute_0_11,plain,
( ~ c_in(v_a,c_insert(v_c,X_15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_in(v_a,c_uminus(c_insert(v_c,X_15,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(subst,[],[cls_Set_OComplD__dest_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_A,$fot(c_insert(v_c,X_15,tc_IntDef_Oint))),bind(V_c,$fot(v_a))]]) ).
cnf(refute_0_12,plain,
c_in(v_c,c_insert(v_c,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(v_c))]]) ).
cnf(refute_0_13,plain,
( ~ c_in(v_c,X_13,tc_IntDef_Oint)
| ~ c_in(v_c,c_uminus(X_13,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(subst,[],[cls_Set_OComplD__dest_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_A,$fot(X_13)),bind(V_c,$fot(v_c))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(v_b,c_uminus(X_11,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_a,c_uminus(X_11,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_c,c_uminus(X_11,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(c_uminus(X_11,tc_set(tc_IntDef_Oint))))]]) ).
cnf(refute_0_15,plain,
( c_in(v_b,X_11,tc_IntDef_Oint)
| c_in(v_b,c_uminus(X_11,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(subst,[],[cls_Set_OComplI_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_A,$fot(X_11)),bind(V_c,$fot(v_b))]]) ).
cnf(refute_0_16,plain,
( c_in(v_a,c_uminus(X_11,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,X_11,tc_IntDef_Oint)
| c_in(v_c,c_uminus(X_11,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_in(v_b,c_uminus(X_11,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( c_in(v_a,c_uminus(X_13,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,X_13,tc_IntDef_Oint)
| c_in(v_c,c_uminus(X_13,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(subst,[],[refute_0_16:[bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_18,plain,
( ~ c_in(v_c,X_13,tc_IntDef_Oint)
| c_in(v_a,c_uminus(X_13,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,X_13,tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_in(v_c,c_uminus(X_13,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) )],[refute_0_17,refute_0_13]) ).
cnf(refute_0_19,plain,
( ~ c_in(v_c,c_insert(v_c,V_B,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_a,c_uminus(c_insert(v_c,V_B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,c_insert(v_c,V_B,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(subst,[],[refute_0_18:[bind(X_13,$fot(c_insert(v_c,V_B,tc_IntDef_Oint)))]]) ).
cnf(refute_0_20,plain,
( c_in(v_a,c_uminus(c_insert(v_c,V_B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,c_insert(v_c,V_B,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_in(v_c,c_insert(v_c,V_B,tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_12,refute_0_19]) ).
cnf(refute_0_21,plain,
( c_in(v_a,c_uminus(c_insert(v_c,X_15,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,c_insert(v_c,X_15,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(subst,[],[refute_0_20:[bind(V_B,$fot(X_15))]]) ).
cnf(refute_0_22,plain,
( ~ c_in(v_a,c_insert(v_c,X_15,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_b,c_insert(v_c,X_15,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_in(v_a,c_uminus(c_insert(v_c,X_15,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) )],[refute_0_21,refute_0_11]) ).
cnf(refute_0_23,plain,
( ~ c_in(v_a,c_insert(v_c,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_b,c_insert(v_c,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(subst,[],[refute_0_22:[bind(X_15,$fot(c_insert(v_a,X_21,tc_IntDef_Oint)))]]) ).
cnf(refute_0_24,plain,
c_in(v_a,c_insert(v_c,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),
inference(subst,[],[refute_0_5:[bind(V_B,$fot(X_21)),bind(X_17,$fot(tc_IntDef_Oint)),bind(X_19,$fot(v_a)),bind(X_20,$fot(v_c))]]) ).
cnf(refute_0_25,plain,
c_in(v_b,c_insert(v_c,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),
inference(resolve,[$cnf( c_in(v_a,c_insert(v_c,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
( ~ c_in(v_b,c_insert(v_c,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| v_b = v_c
| c_in(v_b,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(subst,[],[cls_Set_OinsertE_0:[bind(T_a,$fot(tc_IntDef_Oint)),bind(V_A,$fot(c_insert(v_a,X_21,tc_IntDef_Oint))),bind(V_a,$fot(v_b)),bind(V_b,$fot(v_c))]]) ).
cnf(refute_0_27,plain,
( v_b = v_c
| c_in(v_b,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_in(v_b,c_insert(v_c,c_insert(v_a,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( v_b = v_c
| c_in(v_b,c_insert(v_a,X_62,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(subst,[],[refute_0_27:[bind(X_21,$fot(X_62))]]) ).
cnf(refute_0_29,plain,
( v_b = v_a
| v_b = v_c
| c_in(v_b,X_62,tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_in(v_b,c_insert(v_a,X_62,tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_28,refute_0_10]) ).
cnf(refute_0_30,plain,
( v_b = v_a
| v_b = v_c
| c_in(v_b,c_uminus(V_A,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) ),
inference(subst,[],[refute_0_29:[bind(X_62,$fot(c_uminus(V_A,tc_set(tc_IntDef_Oint))))]]) ).
cnf(refute_0_31,plain,
( ~ c_in(v_b,V_A,tc_IntDef_Oint)
| v_b = v_a
| v_b = v_c ),
inference(resolve,[$cnf( c_in(v_b,c_uminus(V_A,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint) )],[refute_0_30,refute_0_9]) ).
cnf(refute_0_32,plain,
( ~ c_in(v_b,c_insert(V_b,c_insert(X_24,c_insert(v_b,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| v_b = v_a
| v_b = v_c ),
inference(subst,[],[refute_0_31:[bind(V_A,$fot(c_insert(V_b,c_insert(X_24,c_insert(v_b,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)))]]) ).
cnf(refute_0_33,plain,
( v_b = v_a
| v_b = v_c ),
inference(resolve,[$cnf( c_in(v_b,c_insert(V_b,c_insert(X_24,c_insert(v_b,X_21,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )],[refute_0_8,refute_0_32]) ).
cnf(refute_0_34,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( v_b != v_c
| v_c = v_b ),
inference(subst,[],[refute_0_36:[bind(X,$fot(v_b)),bind(Y,$fot(v_c))]]) ).
cnf(refute_0_38,plain,
( v_b = v_a
| v_c = v_b ),
inference(resolve,[$cnf( $equal(v_b,v_c) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
( v_c != v_b
| ~ c_less(v_b,v_c,tc_IntDef_Oint)
| c_less(v_b,v_b,tc_IntDef_Oint) ),
introduced(tautology,[equality,[$cnf( c_less(v_b,v_c,tc_IntDef_Oint) ),[1],$fot(v_b)]]) ).
cnf(refute_0_40,plain,
( ~ c_less(v_b,v_c,tc_IntDef_Oint)
| v_b = v_a
| c_less(v_b,v_b,tc_IntDef_Oint) ),
inference(resolve,[$cnf( $equal(v_c,v_b) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( v_b = v_a
| c_less(v_b,v_b,tc_IntDef_Oint) ),
inference(resolve,[$cnf( c_less(v_b,v_c,tc_IntDef_Oint) )],[cls_conjecture_1,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| v_b = v_a ),
inference(resolve,[$cnf( c_less(v_b,v_b,tc_IntDef_Oint) )],[refute_0_41,refute_0_1]) ).
cnf(refute_0_43,plain,
v_b = v_a,
inference(resolve,[$cnf( class_Orderings_Oorder(tc_IntDef_Oint) )],[clsarity_IntDef__Oint_31,refute_0_42]) ).
cnf(refute_0_44,plain,
( v_b != v_a
| ~ c_less(v_a,v_b,tc_IntDef_Oint)
| c_less(v_a,v_a,tc_IntDef_Oint) ),
introduced(tautology,[equality,[$cnf( c_less(v_a,v_b,tc_IntDef_Oint) ),[1],$fot(v_a)]]) ).
cnf(refute_0_45,plain,
( ~ c_less(v_a,v_b,tc_IntDef_Oint)
| c_less(v_a,v_a,tc_IntDef_Oint) ),
inference(resolve,[$cnf( $equal(v_b,v_a) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
c_less(v_a,v_a,tc_IntDef_Oint),
inference(resolve,[$cnf( c_less(v_a,v_b,tc_IntDef_Oint) )],[cls_conjecture_0,refute_0_45]) ).
cnf(refute_0_47,plain,
~ class_Orderings_Oorder(tc_IntDef_Oint),
inference(resolve,[$cnf( c_less(v_a,v_a,tc_IntDef_Oint) )],[refute_0_46,refute_0_0]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( class_Orderings_Oorder(tc_IntDef_Oint) )],[clsarity_IntDef__Oint_31,refute_0_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET821-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.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 : Mon Jul 11 02:42:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------