%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU224+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 02:19:46 PM UTC 2026
% Result : Theorem 0.22s 0.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 29 ( 6 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 111 ( 39 ~; 39 |; 25 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 31 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f117,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f228,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f638,plain,
? [A,B,C] :
( ( in(B,relation_dom(relation_dom_restriction(C,A)))
<~> ( in(B,A)
& in(B,relation_dom(C)) ) )
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f118]) ).
fof(f639,plain,
? [A,B,C] :
( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& function(C)
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f638]) ).
fof(f640,plain,
? [C] :
( ? [A,B] :
( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_dom_restriction(C,A))) ) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f639]) ).
fof(f641,plain,
( ( ~ in(sK57_skl,sK56_skl)
| ~ in(sK57_skl,relation_dom(sK55_skl))
| ~ in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))) )
& ( ( in(sK57_skl,sK56_skl)
& in(sK57_skl,relation_dom(sK55_skl)) )
| in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))) )
& function(sK55_skl)
& relation(sK55_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl,sK57_skl]),skolemize(C,sK55_skl),skolemize(A,sK56_skl),skolemize(B,sK57_skl)],[f640]) ).
fof(f642,plain,
relation(sK55_skl),
inference(cnf_transformation,[status(thm)],[f641]) ).
fof(f644,plain,
( in(sK57_skl,relation_dom(sK55_skl))
| in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))) ),
inference(cnf_transformation,[status(thm)],[f641]) ).
fof(f645,plain,
( in(sK57_skl,sK56_skl)
| in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))) ),
inference(cnf_transformation,[status(thm)],[f641]) ).
fof(f646,plain,
( ~ in(sK57_skl,sK56_skl)
| ~ in(sK57_skl,relation_dom(sK55_skl))
| ~ in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))) ),
inference(cnf_transformation,[status(thm)],[f641]) ).
fof(f985,plain,
! [A,B,C] :
( ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f228]) ).
fof(f986,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f985]) ).
fof(f987,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ! [A,B] :
( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f986]) ).
fof(f988,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f987]) ).
fof(f989,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f987]) ).
fof(f990,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f987]) ).
fof(f1136,plain,
( in(sK57_skl,sK56_skl)
| in(sK57_skl,sK56_skl)
| ~ relation(sK55_skl) ),
inference(resolution,[status(thm)],[f988,f645]) ).
fof(f1138,plain,
( in(sK57_skl,sK56_skl)
| ~ relation(sK55_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1136]) ).
fof(f1139,plain,
in(sK57_skl,sK56_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1138,f642]) ).
fof(f1141,plain,
( ~ in(sK57_skl,relation_dom(sK55_skl))
| ~ in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))) ),
inference(backward_subsumption_resolution,[status(thm)],[f646,f1139]) ).
fof(f1143,plain,
( in(sK57_skl,relation_dom(sK55_skl))
| in(sK57_skl,relation_dom(sK55_skl))
| ~ relation(sK55_skl) ),
inference(resolution,[status(thm)],[f989,f644]) ).
fof(f1144,plain,
( in(sK57_skl,relation_dom(sK55_skl))
| ~ relation(sK55_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1143]) ).
fof(f1145,plain,
in(sK57_skl,relation_dom(sK55_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f1144,f642]) ).
fof(f1152,plain,
~ in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f1141,f1145]) ).
fof(f1153,plain,
! [X0] :
( ~ in(sK57_skl,X0)
| in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,X0)))
| ~ relation(sK55_skl) ),
inference(resolution,[status(thm)],[f990,f1145]) ).
fof(f1154,plain,
! [X0] :
( ~ in(sK57_skl,X0)
| in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1153,f642]) ).
fof(f1155,plain,
in(sK57_skl,relation_dom(relation_dom_restriction(sK55_skl,sK56_skl))),
inference(resolution,[status(thm)],[f1154,f1139]) ).
fof(f1157,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1155,f1152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU224+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n015.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 06:03:07 UTC 2026
% 0.18/0.49 % CPUTime :
% 0.22/0.53 % Drodi V4.1.1
% 0.22/0.53 % Refutation found
% 0.22/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.63 % Elapsed time: 0.120705 seconds
% 0.27/0.63 % CPU time: 0.134013 seconds
% 0.27/0.63 % Total memory used: 11.561 MB
% 0.27/0.63 % Net memory used: 11.527 MB
%------------------------------------------------------------------------------