TSTP Solution File: SET825-2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 : 300s
% DateTime : Wed May 31 12:35:16 EDT 2023
% Result : Unsatisfiable 0.10s 0.34s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 68 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 27 ~; 29 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 17 (; 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_a,T_a] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_a,V_b,T_a] :
( ~ 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 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_U] :
( 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] :
( 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f8,plain,
! [V_a,V_b] :
( ! [T_a] : ~ 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 ),
inference(miniscoping,[status(esa)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f10,plain,
v_Q(v_n),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f11,plain,
~ v_Q(v_m),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f12,plain,
! [X0] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f13,plain,
! [X0] :
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f14,plain,
( spl0_0
<=> c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(split_symbol_definition) ).
fof(f15,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,plain,
( spl0_1
<=> 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)) ),
introduced(split_symbol_definition) ).
fof(f18,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))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,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(resolution,[status(thm)],[f7,f12]) ).
fof(f21,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f20,f14,f17]) ).
fof(f22,plain,
( v_n = v_m
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f15,f9]) ).
fof(f26,plain,
( ~ v_Q(v_n)
| ~ spl0_0 ),
inference(backward_demodulation,[status(thm)],[f22,f11]) ).
fof(f27,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f10]) ).
fof(f28,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f27]) ).
fof(f31,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f18,f9]) ).
fof(f33,plain,
( spl0_2
<=> 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)) ),
introduced(split_symbol_definition) ).
fof(f35,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))
| spl0_2 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( spl0_3
<=> c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(split_symbol_definition) ).
fof(f38,plain,
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| spl0_3 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,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(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_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f31,f13]) ).
fof(f40,plain,
( spl0_0
| ~ spl0_2
| ~ spl0_3
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f39,f14,f33,f36,f17]) ).
fof(f41,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f7]) ).
fof(f42,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f43,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f7]) ).
fof(f44,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f45,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f28,f40,f42,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n006.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 10:11:17 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 0.10/0.34 % Refutation found
% 0.10/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.56 % Elapsed time: 0.009831 seconds
% 0.14/0.56 % CPU time: 0.010651 seconds
% 0.14/0.56 % Memory used: 2.870 MB
%------------------------------------------------------------------------------