TSTP Solution File: SEU164+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU164+1 : TPTP v8.1.2. Released v3.3.0.
% 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 12:36:04 EDT 2023
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : union(powerset(A)) = A,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f23,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(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)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| ~ in(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| in(X2,X0)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f30,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f31,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)],[f30]) ).
fof(f32,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)],[f31]) ).
fof(f33,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)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f37,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(f38,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)],[f37]) ).
fof(f39,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)],[f38]) ).
fof(f43,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)],[f39]) ).
fof(f44,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)],[f39]) ).
fof(f45,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_4(X0,X1),X0)
| in(sk0_5(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f50,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f51,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f57,plain,
? [A] : union(powerset(A)) != A,
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f58,plain,
union(powerset(sk0_7)) != sk0_7,
inference(skolemization,[status(esa)],[f57]) ).
fof(f59,plain,
union(powerset(sk0_7)) != sk0_7,
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(equality_resolution,[status(esa)],[f26]) ).
fof(f62,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(equality_resolution,[status(esa)],[f27]) ).
fof(f64,plain,
! [X0] : in(X0,powerset(X0)),
inference(resolution,[status(thm)],[f51,f62]) ).
fof(f557,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)],[f43,f45]) ).
fof(f558,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)],[f557]) ).
fof(f559,plain,
! [X0,X1] :
( X0 = union(X1)
| ~ in(X0,X1)
| in(sk0_5(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f45]) ).
fof(f622,plain,
! [X0] :
( X0 = union(powerset(X0))
| in(sk0_5(X0,powerset(X0)),powerset(X0)) ),
inference(resolution,[status(thm)],[f559,f64]) ).
fof(f623,plain,
! [X0] :
( X0 = union(powerset(X0))
| subset(sk0_5(X0,powerset(X0)),X0) ),
inference(resolution,[status(thm)],[f622,f61]) ).
fof(f651,plain,
! [X0,X1] :
( X0 = union(powerset(X0))
| ~ in(X1,sk0_5(X0,powerset(X0)))
| in(X1,X0) ),
inference(resolution,[status(thm)],[f623,f34]) ).
fof(f654,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)],[f651,f44]) ).
fof(f655,plain,
! [X0] :
( X0 = union(powerset(X0))
| in(sk0_4(X0,powerset(X0)),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f654]) ).
fof(f661,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)],[f655,f43]) ).
fof(f662,plain,
! [X0] :
( X0 = union(powerset(X0))
| ~ in(sk0_4(X0,powerset(X0)),X0)
| ~ in(X0,powerset(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f661]) ).
fof(f663,plain,
! [X0] :
( X0 = union(powerset(X0))
| ~ in(X0,powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f662,f655]) ).
fof(f683,plain,
! [X0] : X0 = union(powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f663,f64]) ).
fof(f684,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f59,f683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU164+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue May 30 09:19:15 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % Drodi V3.5.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.159918 seconds
% 0.13/0.45 % CPU time: 1.164406 seconds
% 0.13/0.45 % Memory used: 59.422 MB
%------------------------------------------------------------------------------