TSTP Solution File: SET864-2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET864-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:35:25 EDT 2023
% Result : Unsatisfiable 0.09s 0.34s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 54 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 27 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 19 (; 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_u,V_S,T_a,V_c] :
( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| c_Union(V_c,T_a) = V_u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [V_U] :
( c_in(v_x(V_U),v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_U] :
( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] :
( V_U != v_x(V_U)
| ~ c_in(V_U,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [V_u,T_a,V_c] :
( ! [V_S] :
( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) )
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| c_Union(V_c,T_a) = V_u ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X0,X1,tc_set(X2))
| ~ c_in(X3,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Union(X3,X2),X0,tc_set(X2))
| c_Union(X3,X2) = X0 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f9,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f10,plain,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f11,plain,
! [X0] :
( c_in(v_x(X0),v_S,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f12,plain,
! [X0] :
( c_lessequals(X0,v_x(X0),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f13,plain,
! [X0] :
( X0 != v_x(X0)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f14,plain,
c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f11,f10]) ).
fof(f17,plain,
c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[f12,f10]) ).
fof(f32,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_lessequals(c_Union(v_c,t_a),X0,tc_set(t_a))
| c_Union(v_c,t_a) = X0 ),
inference(resolution,[status(thm)],[f8,f9]) ).
fof(f33,plain,
( spl0_0
<=> c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) ),
introduced(split_symbol_definition) ).
fof(f35,plain,
( ~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a))
| spl0_0 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( spl0_1
<=> c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)) ),
introduced(split_symbol_definition) ).
fof(f37,plain,
( c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( ~ c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a))
| c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)) ),
inference(resolution,[status(thm)],[f32,f17]) ).
fof(f40,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f39,f33,f36]) ).
fof(f41,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f14]) ).
fof(f42,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f88,plain,
( ~ c_in(c_Union(v_c,t_a),v_S,tc_set(t_a))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f37,f13]) ).
fof(f89,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f10]) ).
fof(f90,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f89]) ).
fof(f91,plain,
$false,
inference(sat_refutation,[status(thm)],[f40,f42,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SET864-2 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33 % Computer : n032.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Tue May 30 10:21:16 EDT 2023
% 0.09/0.33 % CPUTime :
% 0.09/0.33 % Drodi V3.5.1
% 0.09/0.34 % Refutation found
% 0.09/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.34 % Elapsed time: 0.011457 seconds
% 0.15/0.56 % CPU time: 0.012436 seconds
% 0.15/0.56 % Memory used: 1.079 MB
%------------------------------------------------------------------------------