TSTP Solution File: SEU217+2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% 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 20:41:32 EDT 2024
% Result : Theorem 0.17s 0.35s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 150 ( 59 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 186 ( 70 ~; 70 |; 32 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 79 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( in(C,A)
& C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B,C] :
( ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) )
& ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f165,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f166,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f165]) ).
fof(f206,lemma,
! [A] :
( relation_dom(identity_relation(A)) = A
& relation_rng(identity_relation(A)) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f235,plain,
! [A,B] :
( ~ relation(B)
| ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( in(C,A)
& C = D ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f236,plain,
! [A,B] :
( ~ relation(B)
| ( ( B != identity_relation(A)
| ! [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| ( in(C,A)
& C = D ) )
& ( in(ordered_pair(C,D),B)
| ~ in(C,A)
| C != D ) ) )
& ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| ~ in(C,A)
| C != D )
& ( in(ordered_pair(C,D),B)
| ( in(C,A)
& C = D ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f235]) ).
fof(f237,plain,
! [B] :
( ~ relation(B)
| ( ! [A] :
( B != identity_relation(A)
| ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| ( in(C,A)
& C = D ) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(C,A)
| C != D ) ) )
& ! [A] :
( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| ~ in(C,A)
| C != D )
& ( in(ordered_pair(C,D),B)
| ( in(C,A)
& C = D ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f236]) ).
fof(f238,plain,
! [B] :
( ~ relation(B)
| ( ! [A] :
( B != identity_relation(A)
| ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| ( in(C,A)
& C = D ) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(C,A)
| C != D ) ) )
& ! [A] :
( B = identity_relation(A)
| ( ( ~ in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)
| ~ in(sk0_0(A,B),A)
| sk0_0(A,B) != sk0_1(A,B) )
& ( in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)
| ( in(sk0_0(A,B),A)
& sk0_0(A,B) = sk0_1(A,B) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f237]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X0 != identity_relation(X1)
| ~ in(ordered_pair(X2,X3),X0)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f238]) ).
fof(f392,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ! [B,C] :
( ( ~ in(B,relation_dom(A))
| ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) )
& ( in(B,relation_dom(A))
| ( C = apply(A,B)
<=> C = empty_set ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f393,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ! [B,C] :
( ( ~ in(B,relation_dom(A))
| ( ( C != apply(A,B)
| in(ordered_pair(B,C),A) )
& ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) ) ) )
& ( in(B,relation_dom(A))
| ( ( C != apply(A,B)
| C = empty_set )
& ( C = apply(A,B)
| C != empty_set ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f392]) ).
fof(f394,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ! [B] :
( ~ in(B,relation_dom(A))
| ( ! [C] :
( C != apply(A,B)
| in(ordered_pair(B,C),A) )
& ! [C] :
( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) ) ) )
& ! [B] :
( in(B,relation_dom(A))
| ( ! [C] :
( C != apply(A,B)
| C = empty_set )
& ! [C] :
( C = apply(A,B)
| C != empty_set ) ) ) ) ),
inference(miniscoping,[status(esa)],[f393]) ).
fof(f395,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| X2 != apply(X0,X1)
| in(ordered_pair(X1,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f394]) ).
fof(f483,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f512,plain,
( ! [A] : relation(identity_relation(A))
& ! [A] : function(identity_relation(A)) ),
inference(miniscoping,[status(esa)],[f78]) ).
fof(f514,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f512]) ).
fof(f765,plain,
? [A,B] :
( in(B,A)
& apply(identity_relation(A),B) != B ),
inference(pre_NNF_transformation,[status(esa)],[f166]) ).
fof(f766,plain,
( in(sk0_67,sk0_66)
& apply(identity_relation(sk0_66),sk0_67) != sk0_67 ),
inference(skolemization,[status(esa)],[f765]) ).
fof(f767,plain,
in(sk0_67,sk0_66),
inference(cnf_transformation,[status(esa)],[f766]) ).
fof(f768,plain,
apply(identity_relation(sk0_66),sk0_67) != sk0_67,
inference(cnf_transformation,[status(esa)],[f766]) ).
fof(f872,plain,
( ! [A] : relation_dom(identity_relation(A)) = A
& ! [A] : relation_rng(identity_relation(A)) = A ),
inference(miniscoping,[status(esa)],[f206]) ).
fof(f873,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f872]) ).
fof(f942,plain,
! [X0,X1,X2] :
( ~ relation(identity_relation(X0))
| ~ in(ordered_pair(X1,X2),identity_relation(X0))
| X1 = X2 ),
inference(destructive_equality_resolution,[status(esa)],[f240]) ).
fof(f979,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f395]) ).
fof(f1011,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X0,X1),identity_relation(X2))
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f942,f483]) ).
fof(f1016,plain,
! [X0,X1] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| ~ in(X1,relation_dom(identity_relation(X0)))
| X1 = apply(identity_relation(X0),X1) ),
inference(resolution,[status(thm)],[f979,f1011]) ).
fof(f1017,plain,
! [X0,X1] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| ~ in(X1,X0)
| X1 = apply(identity_relation(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f873,f1016]) ).
fof(f1018,plain,
! [X0,X1] :
( ~ function(identity_relation(X0))
| ~ in(X1,X0)
| X1 = apply(identity_relation(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1017,f483]) ).
fof(f1028,plain,
! [X0,X1] :
( ~ in(X0,X1)
| X0 = apply(identity_relation(X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1018,f514]) ).
fof(f1029,plain,
~ in(sk0_67,sk0_66),
inference(resolution,[status(thm)],[f1028,f768]) ).
fof(f1030,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1029,f767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 19:34:34 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.35 % Drodi V3.6.0
% 0.17/0.35 % Refutation found
% 0.17/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.38 % Elapsed time: 0.037480 seconds
% 0.17/0.38 % CPU time: 0.049319 seconds
% 0.17/0.38 % Total memory used: 19.032 MB
% 0.17/0.38 % Net memory used: 18.956 MB
%------------------------------------------------------------------------------