TSTP Solution File: SET840-2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET840-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 : Tue Apr 30 20:40:30 EDT 2024
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 10 unt; 0 def)
% Number of atoms : 122 ( 35 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 122 ( 52 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 140 ( 140 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : ~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] :
( c_lessequals(c_Union(v_S,t_b),V_U,tc_set(t_b))
| ~ c_in(V_U,v_S,tc_set(t_b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_A,V_X,T_a,V_C] :
( ~ c_in(V_A,V_X,T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_a,V_B,T_a,V_b] :
( ~ c_in(V_a,V_B,T_a)
| c_in(V_a,c_insert(V_b,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_a,V_b,V_A,T_a] :
( ~ 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 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_A,V_B,T_a] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_A,V_B,T_a] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_B,V_A,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| V_A = V_B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f11,plain,
! [X0] :
( c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b))
| ~ c_in(X0,v_S,tc_set(t_b)) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f12,plain,
! [V_A,T_a,V_C] :
( ! [V_X] :
( ~ c_in(V_A,V_X,T_a)
| ~ c_in(V_X,V_C,tc_set(T_a)) )
| c_in(V_A,c_Union(V_C,T_a),T_a) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X0,X1,X2)
| ~ c_in(X1,X3,tc_set(X2))
| c_in(X0,c_Union(X3,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f14,plain,
! [V_a,V_B,T_a] :
( ~ c_in(V_a,V_B,T_a)
| ! [V_b] : c_in(V_a,c_insert(V_b,V_B,T_a),T_a) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_insert(X3,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f17,plain,
! [V_a,V_b] :
( ! [V_A,T_a] :
( ~ 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 ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X0,c_insert(X1,X2,X3),X3)
| c_in(X0,X2,X3)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f21,plain,
! [V_B,V_A] :
( ! [T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) )
| V_A = V_B ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,c_Union(X1,X2),X2),X3,X2)
| ~ c_in(X3,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f20,f13]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X0,c_insert(X1,X2,X3),tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X0,c_insert(X1,X2,X3),X3),X2,X3) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),c_insert(X3,X1,X2),X2)
| c_Main_OsubsetI__1(X0,X1,X2) = X3 ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_insert(X1,X2,X3),X3),X2,X3)
| ~ c_lessequals(c_insert(X1,X2,X3),X0,tc_set(X3))
| X0 = c_insert(X1,X2,X3) ),
inference(resolution,[status(thm)],[f38,f22]) ).
fof(f43,plain,
! [X0,X1,X2] :
( c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2))
| c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f39,f19]) ).
fof(f44,plain,
! [X0,X1,X2] :
( c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2))
| c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0 ),
inference(duplicate_literals_removal,[status(esa)],[f43]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(X1,X2),X2),X3,X2)
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_lessequals(c_Union(X1,X2),X0,tc_set(X2))
| X0 = c_Union(X1,X2) ),
inference(resolution,[status(thm)],[f37,f22]) ).
fof(f54,plain,
! [X0,X1,X2] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| ~ c_in(c_Main_OsubsetI__1(X1,c_insert(X0,X1,X2),X2),X1,X2)
| X1 = c_insert(X0,X1,X2) ),
inference(resolution,[status(thm)],[f44,f41]) ).
fof(f56,plain,
! [X0,X1,X2] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| ~ c_lessequals(X1,c_insert(X0,X1,X2),tc_set(X2))
| c_insert(X0,X1,X2) = X1 ),
inference(resolution,[status(thm)],[f44,f22]) ).
fof(f59,plain,
! [X0,X1,X2] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| X1 = c_insert(X0,X1,X2)
| c_lessequals(X1,c_insert(X0,X1,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[f54,f19]) ).
fof(f60,plain,
! [X0,X1,X2] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X1,X2) = X0
| X1 = c_insert(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f56]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| c_lessequals(c_insert(X0,X1,X2),X1,tc_set(X2))
| X1 = c_insert(X0,X1,X2) ),
inference(paramodulation,[status(thm)],[f60,f20]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| X1 = c_insert(X0,X1,X2)
| ~ c_in(c_Main_OsubsetI__1(X1,c_insert(X0,X1,X2),X2),X1,X2)
| X1 = c_insert(X0,X1,X2) ),
inference(resolution,[status(thm)],[f65,f41]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| X1 = c_insert(X0,X1,X2)
| ~ c_in(c_Main_OsubsetI__1(X1,c_insert(X0,X1,X2),X2),X1,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f67]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| X1 = c_insert(X0,X1,X2)
| ~ c_lessequals(X1,c_insert(X0,X1,X2),tc_set(X2))
| c_insert(X0,X1,X2) = X1 ),
inference(resolution,[status(thm)],[f65,f22]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| X1 = c_insert(X0,X1,X2)
| ~ c_lessequals(X1,c_insert(X0,X1,X2),tc_set(X2)) ),
inference(duplicate_literals_removal,[status(esa)],[f71]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| X1 = c_insert(X0,X1,X2)
| c_lessequals(X1,c_insert(X0,X1,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[f68,f19]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,X2)
| X1 = c_insert(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f72]) ).
fof(f80,plain,
! [X0,X1,X2] :
( X0 = c_insert(c_Main_OsubsetI__1(X0,X1,X2),X0,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f76,f19]) ).
fof(f97,plain,
! [X0] : v_S = c_insert(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),v_S,tc_set(t_b)),
inference(resolution,[status(thm)],[f80,f10]) ).
fof(f163,plain,
! [X0] : c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),v_S,tc_set(t_b)),
inference(paramodulation,[status(thm)],[f97,f16]) ).
fof(f164,plain,
! [X0] : c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),tc_set(t_b)),
inference(resolution,[status(thm)],[f163,f11]) ).
fof(f165,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_Union(v_S,t_b),t_b),c_Main_OsubsetI__1(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(t_b)),t_b)
| ~ c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b))
| X0 = c_Union(v_S,t_b) ),
inference(resolution,[status(thm)],[f163,f49]) ).
fof(f169,plain,
! [X0] :
( ~ c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b))
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(resolution,[status(thm)],[f164,f22]) ).
fof(f230,plain,
! [X0] :
( ~ c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),tc_set(t_b))
| c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b)
| c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b)) ),
inference(resolution,[status(thm)],[f165,f19]) ).
fof(f231,plain,
! [X0] :
( c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b)
| c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b)) ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f164]) ).
fof(f242,plain,
! [X0] : c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b),
inference(forward_subsumption_resolution,[status(thm)],[f231,f169]) ).
fof(f276,plain,
! [X0] :
( ~ c_in(c_Union(v_S,t_b),c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) ),
inference(paramodulation,[status(thm)],[f242,f20]) ).
fof(f277,plain,
! [X0] : ~ c_in(c_Union(v_S,t_b),c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(forward_subsumption_resolution,[status(thm)],[f276,f10]) ).
fof(f454,plain,
$false,
inference(resolution,[status(thm)],[f277,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET840-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 22:06:58 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.060412 seconds
% 0.14/0.40 % CPU time: 0.383270 seconds
% 0.14/0.40 % Total memory used: 59.805 MB
% 0.14/0.40 % Net memory used: 59.478 MB
%------------------------------------------------------------------------------