TSTP Solution File: SEU325+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU325+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 12:36:42 EDT 2023
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 80 ( 21 unt; 0 def)
% Number of atoms : 216 ( 30 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 220 ( 84 ~; 78 |; 38 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 7 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 92 (; 81 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
( empty(empty_set)
& v1_membered(empty_set)
& v2_membered(empty_set)
& v3_membered(empty_set)
& v4_membered(empty_set)
& v5_membered(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( is_a_cover_of_carrier(A,B)
& B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( is_a_cover_of_carrier(A,B)
& B = empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,plain,
! [A,B] :
( ( B != union(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) )
& ( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) )
& ( in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f18]) ).
fof(f110,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) )
& ( in(C,B)
| ? [D] :
( in(C,D)
& in(D,A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f109]) ).
fof(f111,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ( in(C,sk0_0(C,B,A))
& in(sk0_0(C,B,A),A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ( ( ~ in(sk0_1(B,A),B)
| ! [D] :
( ~ in(sk0_1(B,A),D)
| ~ in(D,A) ) )
& ( in(sk0_1(B,A),B)
| ( in(sk0_1(B,A),sk0_2(B,A))
& in(sk0_2(B,A),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f110]) ).
fof(f113,plain,
! [X0,X1,X2] :
( X0 != union(X1)
| ~ in(X2,X0)
| in(sk0_0(X2,X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f118,plain,
! [A] :
( ~ one_sorted_str(A)
| ! [B] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f119,plain,
! [A] :
( ~ one_sorted_str(A)
| ! [B] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ( ( ~ is_a_cover_of_carrier(A,B)
| cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) )
& ( is_a_cover_of_carrier(A,B)
| cast_as_carrier_subset(A) != union_of_subsets(the_carrier(A),B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ is_a_cover_of_carrier(X0,X1)
| cast_as_carrier_subset(X0) = union_of_subsets(the_carrier(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f119]) ).
fof(f128,plain,
! [A] : element(sk0_4(A),A),
inference(skolemization,[status(esa)],[f29]) ).
fof(f129,plain,
! [X0] : element(sk0_4(X0),X0),
inference(cnf_transformation,[status(esa)],[f128]) ).
fof(f133,plain,
! [A] :
( empty_carrier(A)
| ~ one_sorted_str(A)
| ~ empty(cast_as_carrier_subset(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f134,plain,
! [X0] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(cast_as_carrier_subset(X0)) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f135,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f152,plain,
! [A] :
( element(sk0_7(A),powerset(A))
& empty(sk0_7(A)) ),
inference(skolemization,[status(esa)],[f36]) ).
fof(f153,plain,
! [X0] : element(sk0_7(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f152]) ).
fof(f154,plain,
! [X0] : empty(sk0_7(X0)),
inference(cnf_transformation,[status(esa)],[f152]) ).
fof(f162,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| union_of_subsets(A,B) = union(B) ),
inference(pre_NNF_transformation,[status(esa)],[f39]) ).
fof(f163,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| union_of_subsets(X1,X0) = union(X0) ),
inference(cnf_transformation,[status(esa)],[f162]) ).
fof(f168,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f169,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f168]) ).
fof(f180,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A)
& ? [B] :
( element(B,powerset(powerset(the_carrier(A))))
& is_a_cover_of_carrier(A,B)
& B = empty_set ) ),
inference(pre_NNF_transformation,[status(esa)],[f47]) ).
fof(f181,plain,
( ~ empty_carrier(sk0_10)
& one_sorted_str(sk0_10)
& element(sk0_11,powerset(powerset(the_carrier(sk0_10))))
& is_a_cover_of_carrier(sk0_10,sk0_11)
& sk0_11 = empty_set ),
inference(skolemization,[status(esa)],[f180]) ).
fof(f182,plain,
~ empty_carrier(sk0_10),
inference(cnf_transformation,[status(esa)],[f181]) ).
fof(f183,plain,
one_sorted_str(sk0_10),
inference(cnf_transformation,[status(esa)],[f181]) ).
fof(f184,plain,
element(sk0_11,powerset(powerset(the_carrier(sk0_10)))),
inference(cnf_transformation,[status(esa)],[f181]) ).
fof(f185,plain,
is_a_cover_of_carrier(sk0_10,sk0_11),
inference(cnf_transformation,[status(esa)],[f181]) ).
fof(f186,plain,
sk0_11 = empty_set,
inference(cnf_transformation,[status(esa)],[f181]) ).
fof(f187,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f48]) ).
fof(f188,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f187]) ).
fof(f189,plain,
! [A,B] :
( ~ in(A,B)
| ~ empty(B) ),
inference(pre_NNF_transformation,[status(esa)],[f49]) ).
fof(f190,plain,
! [B] :
( ! [A] : ~ in(A,B)
| ~ empty(B) ),
inference(miniscoping,[status(esa)],[f189]) ).
fof(f191,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[status(esa)],[f190]) ).
fof(f196,plain,
! [X0,X1] :
( ~ in(X0,union(X1))
| in(sk0_0(X0,union(X1),X1),X1) ),
inference(destructive_equality_resolution,[status(esa)],[f113]) ).
fof(f198,plain,
is_a_cover_of_carrier(sk0_10,empty_set),
inference(forward_demodulation,[status(thm)],[f186,f185]) ).
fof(f199,plain,
element(empty_set,powerset(powerset(the_carrier(sk0_10)))),
inference(forward_demodulation,[status(thm)],[f186,f184]) ).
fof(f200,plain,
( spl0_0
<=> one_sorted_str(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f202,plain,
( ~ one_sorted_str(sk0_10)
| spl0_0 ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( spl0_1
<=> is_a_cover_of_carrier(sk0_10,empty_set) ),
introduced(split_symbol_definition) ).
fof(f205,plain,
( ~ is_a_cover_of_carrier(sk0_10,empty_set)
| spl0_1 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( spl0_2
<=> cast_as_carrier_subset(sk0_10) = union_of_subsets(the_carrier(sk0_10),empty_set) ),
introduced(split_symbol_definition) ).
fof(f207,plain,
( cast_as_carrier_subset(sk0_10) = union_of_subsets(the_carrier(sk0_10),empty_set)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( ~ one_sorted_str(sk0_10)
| ~ is_a_cover_of_carrier(sk0_10,empty_set)
| cast_as_carrier_subset(sk0_10) = union_of_subsets(the_carrier(sk0_10),empty_set) ),
inference(resolution,[status(thm)],[f120,f199]) ).
fof(f210,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f209,f200,f203,f206]) ).
fof(f211,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f198]) ).
fof(f212,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f183]) ).
fof(f214,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f223,plain,
! [X0] : sk0_7(X0) = empty_set,
inference(resolution,[status(thm)],[f154,f188]) ).
fof(f271,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f223,f153]) ).
fof(f400,plain,
! [X0] :
( empty(X0)
| in(sk0_4(X0),X0) ),
inference(resolution,[status(thm)],[f169,f129]) ).
fof(f622,plain,
! [X0,X1] :
( ~ in(X0,union(X1))
| ~ empty(X1) ),
inference(resolution,[status(thm)],[f196,f191]) ).
fof(f625,plain,
! [X0] :
( ~ empty(X0)
| empty(union(X0)) ),
inference(resolution,[status(thm)],[f622,f400]) ).
fof(f750,plain,
! [X0] : union_of_subsets(X0,empty_set) = union(empty_set),
inference(resolution,[status(thm)],[f163,f271]) ).
fof(f871,plain,
( spl0_50
<=> empty(cast_as_carrier_subset(sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f872,plain,
( empty(cast_as_carrier_subset(sk0_10))
| ~ spl0_50 ),
inference(component_clause,[status(thm)],[f871]) ).
fof(f909,plain,
( spl0_56
<=> empty_carrier(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f910,plain,
( empty_carrier(sk0_10)
| ~ spl0_56 ),
inference(component_clause,[status(thm)],[f909]) ).
fof(f917,plain,
( empty_carrier(sk0_10)
| ~ one_sorted_str(sk0_10)
| ~ spl0_50 ),
inference(resolution,[status(thm)],[f872,f134]) ).
fof(f918,plain,
( spl0_56
| ~ spl0_0
| ~ spl0_50 ),
inference(split_clause,[status(thm)],[f917,f909,f200,f871]) ).
fof(f926,plain,
( $false
| ~ spl0_56 ),
inference(forward_subsumption_resolution,[status(thm)],[f910,f182]) ).
fof(f927,plain,
~ spl0_56,
inference(contradiction_clause,[status(thm)],[f926]) ).
fof(f1025,plain,
( cast_as_carrier_subset(sk0_10) = union(empty_set)
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f750,f207]) ).
fof(f1050,plain,
( spl0_72
<=> empty(empty_set) ),
introduced(split_symbol_definition) ).
fof(f1052,plain,
( ~ empty(empty_set)
| spl0_72 ),
inference(component_clause,[status(thm)],[f1050]) ).
fof(f1069,plain,
( ~ empty(empty_set)
| empty(cast_as_carrier_subset(sk0_10))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f1025,f625]) ).
fof(f1070,plain,
( ~ spl0_72
| spl0_50
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f1069,f1050,f871,f206]) ).
fof(f1080,plain,
( $false
| spl0_72 ),
inference(forward_subsumption_resolution,[status(thm)],[f1052,f135]) ).
fof(f1081,plain,
spl0_72,
inference(contradiction_clause,[status(thm)],[f1080]) ).
fof(f1082,plain,
$false,
inference(sat_refutation,[status(thm)],[f210,f212,f214,f918,f927,f1070,f1081]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU325+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n010.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 : 300
% 0.13/0.34 % DateTime : Tue May 30 09:02:07 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.5.1
% 0.19/0.37 % Refutation found
% 0.19/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.38 % Elapsed time: 0.037567 seconds
% 0.19/0.38 % CPU time: 0.134883 seconds
% 0.19/0.38 % Memory used: 19.834 MB
%------------------------------------------------------------------------------