%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:44 PM UTC 2026
% Result : Theorem 0.08s 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 75 ( 35 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 88 ( 35 ~; 31 |; 16 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f73,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f75,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f81,plain,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f82,plain,
( apply(identity_relation(sK7_skl),sK8_skl) != sK8_skl
& in(sK8_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f81]) ).
fof(f83,plain,
in(sK8_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
apply(identity_relation(sK7_skl),sK8_skl) != sK8_skl,
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A ) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f86,plain,
! [A,B] :
( ( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [B] :
( ( ! [A] :
( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f88,plain,
! [B] :
( ( ! [A] :
( ( apply(B,sK9_skl(A,B)) != sK9_skl(A,B)
& in(sK9_skl(A,B),A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(C,sK9_skl(A,B))],[f87]) ).
fof(f90,plain,
! [X0,X1,X2] :
( apply(X0,X2) = X2
| ~ in(X2,X1)
| X0 != identity_relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f94,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f90]) ).
fof(f98,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f69]) ).
fof(f103,plain,
! [X0,X1] :
( apply(identity_relation(X1),X0) = X0
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f98,f75]) ).
fof(f104,plain,
apply(identity_relation(sK7_skl),sK8_skl) = sK8_skl,
inference(resolution,[status(thm)],[f103,f83]) ).
fof(f105,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f104,f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 06:01:51 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.41 % Drodi V4.1.1
% 0.08/0.42 % Refutation found
% 0.08/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.089718 seconds
% 0.14/0.48 % CPU time: 0.102118 seconds
% 0.14/0.48 % Total memory used: 5.057 MB
% 0.14/0.48 % Net memory used: 5.053 MB
%------------------------------------------------------------------------------