TSTP Solution File: SET890+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 20:40:39 EDT 2024
% Result : Theorem 2.71s 0.66s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 138 ( 56 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 164 ( 59 ~; 76 |; 25 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 86 ( 76 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
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,conjecture,
! [A] : union(singleton(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A] : union(singleton(A)) = A,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f19,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f21,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f35,plain,
( ! [A,B] :
( B != union(A)
| ( ! [C] :
( ~ in(C,B)
| ( in(C,sk0_2(C,B,A))
& in(sk0_2(C,B,A),A) ) )
& ! [C] :
( in(C,B)
| ! [D] :
( ~ in(C,D)
| ~ in(D,A) ) ) ) )
& ! [A,B] :
( B = union(A)
| ( ( ~ in(sk0_3(B,A),B)
| ! [D] :
( ~ in(sk0_3(B,A),D)
| ~ in(D,A) ) )
& ( in(sk0_3(B,A),B)
| ( in(sk0_3(B,A),sk0_4(B,A))
& in(sk0_4(B,A),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f34]) ).
fof(f39,plain,
! [X0,X1,X2] :
( X0 = union(X1)
| ~ in(sk0_3(X0,X1),X0)
| ~ in(sk0_3(X0,X1),X2)
| ~ in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_3(X0,X1),X0)
| in(sk0_3(X0,X1),sk0_4(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f41,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_3(X0,X1),X0)
| in(sk0_4(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f50,plain,
? [A] : union(singleton(A)) != A,
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f51,plain,
union(singleton(sk0_7)) != sk0_7,
inference(skolemization,[status(esa)],[f50]) ).
fof(f52,plain,
union(singleton(sk0_7)) != sk0_7,
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( X0 != singleton(X1)
| in(X1,X0) ),
inference(destructive_equality_resolution,[status(esa)],[f23]) ).
fof(f56,plain,
! [X0] : in(X0,singleton(X0)),
inference(equality_resolution,[status(esa)],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(esa)],[f22]) ).
fof(f772,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_4(X0,X1),X1)
| X0 = union(X1)
| ~ in(sk0_3(X0,X1),X0)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f41,f39]) ).
fof(f773,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_4(X0,X1),X1)
| ~ in(sk0_3(X0,X1),X0)
| ~ in(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f772]) ).
fof(f774,plain,
! [X0,X1] :
( X0 = union(X1)
| in(sk0_4(X0,X1),X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f773,f41]) ).
fof(f829,plain,
! [X0] :
( X0 = union(singleton(X0))
| in(sk0_4(X0,singleton(X0)),singleton(X0)) ),
inference(resolution,[status(thm)],[f774,f56]) ).
fof(f832,plain,
! [X0] :
( X0 = union(singleton(X0))
| sk0_4(X0,singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f829,f57]) ).
fof(f860,plain,
! [X0] :
( X0 = union(singleton(X0))
| in(sk0_3(X0,singleton(X0)),X0)
| in(sk0_3(X0,singleton(X0)),X0)
| X0 = union(singleton(X0)) ),
inference(paramodulation,[status(thm)],[f832,f40]) ).
fof(f861,plain,
! [X0] :
( X0 = union(singleton(X0))
| in(sk0_3(X0,singleton(X0)),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f860]) ).
fof(f862,plain,
! [X0] :
( X0 = union(singleton(X0))
| X0 = union(singleton(X0))
| ~ in(sk0_3(X0,singleton(X0)),X0)
| ~ in(X0,singleton(X0)) ),
inference(resolution,[status(thm)],[f861,f39]) ).
fof(f863,plain,
! [X0] :
( X0 = union(singleton(X0))
| ~ in(sk0_3(X0,singleton(X0)),X0)
| ~ in(X0,singleton(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f862]) ).
fof(f864,plain,
! [X0] :
( X0 = union(singleton(X0))
| ~ in(X0,singleton(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f863,f861]) ).
fof(f883,plain,
! [X0] : X0 = union(singleton(X0)),
inference(resolution,[status(thm)],[f864,f56]) ).
fof(f884,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f52,f883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27 % Computer : n002.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Apr 29 22:09:39 EDT 2024
% 0.07/0.27 % CPUTime :
% 0.07/0.28 % Drodi V3.6.0
% 2.71/0.66 % Refutation found
% 2.71/0.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.71/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.71/0.68 % Elapsed time: 0.402500 seconds
% 2.71/0.68 % CPU time: 3.114259 seconds
% 2.71/0.68 % Total memory used: 90.347 MB
% 2.71/0.68 % Net memory used: 88.601 MB
%------------------------------------------------------------------------------