TSTP Solution File: SET825-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:37:30 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 9 unt; 10 nHn; 28 RR)
% Number of literals : 62 ( 23 equ; 23 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Relation_OIdI_0,axiom,
c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)) ).
cnf(cls_Relation_Opair__in__Id__conv__iff1_0,axiom,
( ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a))
| V_a = V_b ) ).
cnf(cls_conjecture_0,negated_conjecture,
v_Q(v_n) ).
cnf(cls_conjecture_1,negated_conjecture,
~ v_Q(v_m) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(V_U),v_xa(V_U),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(V_U)),c_Suc(v_xa(V_U)),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ) ).
cnf(refute_0_0,plain,
( ~ c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_n = v_m ),
inference(subst,[],[cls_Relation_Opair__in__Id__conv__iff1_0:[bind(T_a,$fot(tc_nat)),bind(V_a,$fot(v_n)),bind(V_b,$fot(v_m))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(subst,[],[cls_conjecture_3:[bind(V_U,$fot(c_Relation_OId))]]) ).
cnf(refute_0_2,plain,
( ~ c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
inference(subst,[],[cls_Relation_Opair__in__Id__conv__iff1_0:[bind(T_a,$fot(tc_nat)),bind(V_a,$fot(v_x(c_Relation_OId))),bind(V_b,$fot(v_xa(c_Relation_OId)))]]) ).
cnf(refute_0_3,plain,
c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(subst,[],[cls_Relation_OIdI_0:[bind(T_a,$fot(tc_nat)),bind(V_a,$fot(c_0))]]) ).
cnf(refute_0_4,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(c_Relation_OId))]]) ).
cnf(refute_0_5,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[$cnf( c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) )],[refute_0_5,refute_0_2]) ).
cnf(refute_0_7,plain,
( v_n = v_m
| v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
inference(resolve,[$cnf( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( v_x(c_Relation_OId) != v_xa(c_Relation_OId)
| v_xa(c_Relation_OId) = v_x(c_Relation_OId) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(v_x(c_Relation_OId))),bind(Y,$fot(v_xa(c_Relation_OId)))]]) ).
cnf(refute_0_12,plain,
( v_n = v_m
| v_xa(c_Relation_OId) = v_x(c_Relation_OId) ),
inference(resolve,[$cnf( $equal(v_x(c_Relation_OId),v_xa(c_Relation_OId)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( v_xa(c_Relation_OId) != v_x(c_Relation_OId)
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(tautology,[equality,[$cnf( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),[0,1,0],$fot(v_x(c_Relation_OId))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_n = v_m
| c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[$cnf( $equal(v_xa(c_Relation_OId),v_x(c_Relation_OId)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_n = v_m
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[$cnf( c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) )],[refute_0_14,refute_0_1]) ).
cnf(refute_0_16,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| v_n = v_m
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[$cnf( c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)),
inference(subst,[],[cls_Relation_OIdI_0:[bind(T_a,$fot(tc_nat)),bind(V_a,$fot(c_Suc(v_x(c_Relation_OId))))]]) ).
cnf(refute_0_18,plain,
( v_n = v_m
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolve,[$cnf( c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
v_n = v_m,
inference(resolve,[$cnf( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) )],[refute_0_18,refute_0_0]) ).
cnf(refute_0_20,plain,
( v_n != v_m
| ~ v_Q(v_n)
| v_Q(v_m) ),
introduced(tautology,[equality,[$cnf( v_Q(v_n) ),[0],$fot(v_m)]]) ).
cnf(refute_0_21,plain,
( ~ v_Q(v_n)
| v_Q(v_m) ),
inference(resolve,[$cnf( $equal(v_n,v_m) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
v_Q(v_m),
inference(resolve,[$cnf( v_Q(v_n) )],[cls_conjecture_0,refute_0_21]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( v_Q(v_m) )],[refute_0_22,cls_conjecture_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET825-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 06:02:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------