TSTP Solution File: SEU164+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 20:41:18 EDT 2024
% Result : Theorem 3.69s 0.86s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 171 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 200 ( 72 ~; 90 |; 31 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 116 ( 104 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A] : union(powerset(A)) = A,
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f22,plain,
! [A,B] :
( ( B != powerset(A)
| ! [C] :
( ( ~ in(C,B)
| subset(C,A) )
& ( in(C,B)
| ~ subset(C,A) ) ) )
& ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f23,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ( ( ~ in(sk0_1(B,A),B)
| ~ subset(sk0_1(B,A),A) )
& ( in(sk0_1(B,A),B)
| subset(sk0_1(B,A),A) ) ) ) ),
inference(skolemization,[status(esa)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| ~ in(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| in(X2,X0)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f29,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f30,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_2(B,A),A)
& ~ in(sk0_2(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f36,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)],[f5]) ).
fof(f37,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)],[f36]) ).
fof(f38,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ( in(C,sk0_3(C,B,A))
& in(sk0_3(C,B,A),A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ( ( ~ in(sk0_4(B,A),B)
| ! [D] :
( ~ in(sk0_4(B,A),D)
| ~ in(D,A) ) )
& ( in(sk0_4(B,A),B)
| ( in(sk0_4(B,A),sk0_5(B,A))
& in(sk0_5(B,A),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f42,plain,
! [X0,X1,X2] :
( X0 = union(X1)
| ~ in(sk0_4(X0,X1),X0)
| ~ in(sk0_4(X0,X1),X2)
| ~ in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f43,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_4(X0,X1),X0)
| in(sk0_4(X0,X1),sk0_5(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f44,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_4(X0,X1),X0)
| in(sk0_5(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f53,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f54,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f60,plain,
? [A] : union(powerset(A)) != A,
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f61,plain,
union(powerset(sk0_9)) != sk0_9,
inference(skolemization,[status(esa)],[f60]) ).
fof(f62,plain,
union(powerset(sk0_9)) != sk0_9,
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f64,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(equality_resolution,[status(esa)],[f25]) ).
fof(f65,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(equality_resolution,[status(esa)],[f26]) ).
fof(f67,plain,
! [X0] : in(X0,powerset(X0)),
inference(resolution,[status(thm)],[f54,f65]) ).
fof(f707,plain,
! [X0,X1] :
( X0 = union(X1)
| ~ in(sk0_4(X0,X1),X0)
| ~ in(X0,X1)
| X0 = union(X1)
| in(sk0_5(X0,X1),X1) ),
inference(resolution,[status(thm)],[f42,f44]) ).
fof(f708,plain,
! [X0,X1] :
( X0 = union(X1)
| ~ in(sk0_4(X0,X1),X0)
| ~ in(X0,X1)
| in(sk0_5(X0,X1),X1) ),
inference(duplicate_literals_removal,[status(esa)],[f707]) ).
fof(f709,plain,
! [X0,X1] :
( X0 = union(X1)
| ~ in(X0,X1)
| in(sk0_5(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f44]) ).
fof(f761,plain,
! [X0] :
( X0 = union(powerset(X0))
| in(sk0_5(X0,powerset(X0)),powerset(X0)) ),
inference(resolution,[status(thm)],[f709,f67]) ).
fof(f809,plain,
! [X0] :
( X0 = union(powerset(X0))
| subset(sk0_5(X0,powerset(X0)),X0) ),
inference(resolution,[status(thm)],[f761,f64]) ).
fof(f821,plain,
! [X0,X1] :
( X0 = union(powerset(X0))
| ~ in(X1,sk0_5(X0,powerset(X0)))
| in(X1,X0) ),
inference(resolution,[status(thm)],[f809,f33]) ).
fof(f826,plain,
! [X0] :
( X0 = union(powerset(X0))
| in(sk0_4(X0,powerset(X0)),X0)
| X0 = union(powerset(X0))
| in(sk0_4(X0,powerset(X0)),X0) ),
inference(resolution,[status(thm)],[f821,f43]) ).
fof(f827,plain,
! [X0] :
( X0 = union(powerset(X0))
| in(sk0_4(X0,powerset(X0)),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f826]) ).
fof(f834,plain,
! [X0] :
( X0 = union(powerset(X0))
| X0 = union(powerset(X0))
| ~ in(sk0_4(X0,powerset(X0)),X0)
| ~ in(X0,powerset(X0)) ),
inference(resolution,[status(thm)],[f827,f42]) ).
fof(f835,plain,
! [X0] :
( X0 = union(powerset(X0))
| ~ in(sk0_4(X0,powerset(X0)),X0)
| ~ in(X0,powerset(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f834]) ).
fof(f836,plain,
! [X0] :
( X0 = union(powerset(X0))
| ~ in(X0,powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f835,f827]) ).
fof(f868,plain,
! [X0] : X0 = union(powerset(X0)),
inference(resolution,[status(thm)],[f836,f67]) ).
fof(f869,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f62,f868]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.03/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 19:35:19 EDT 2024
% 0.21/0.35 % CPUTime :
% 0.21/0.37 % Drodi V3.6.0
% 3.69/0.86 % Refutation found
% 3.69/0.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.69/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.69/0.89 % Elapsed time: 0.516767 seconds
% 3.69/0.89 % CPU time: 3.887184 seconds
% 3.69/0.89 % Total memory used: 84.112 MB
% 3.69/0.89 % Net memory used: 82.130 MB
%------------------------------------------------------------------------------