%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV572+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:33:02 PM UTC 2026
% Result : Theorem 47.94s 6.88s
% Output : CNFRefutation 47.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 8
% Syntax : Number of formulae : 81 ( 19 unt; 0 def)
% Number of atoms : 262 ( 98 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 244 ( 63 ~; 162 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 124 ( 122 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subq(X,Y)
<=> ! [Z] :
( mem(Z,X)
=> mem(Z,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subq(X,Y)
=> ( subq(Y,X)
=> X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : ~ mem(X,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( mem(X,s(Y))
<=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] :
( mem(X,u(Y,Z))
<=> ( mem(X,Z)
| mem(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : a(X,Y) = u(X,s(Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : n(X) = a(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
~ subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ ~ subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
! [X,Y] :
( subq(X,Y)
<=> ! [Z] :
( mem(Z,Y)
| ~ mem(Z,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f29,plain,
! [X,Y] :
( ( ? [Z] :
( ~ mem(Z,Y)
& mem(Z,X) )
| subq(X,Y) )
& ( ! [Z] :
( mem(Z,Y)
| ~ mem(Z,X) )
| ~ subq(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [X,Y] :
( ? [Z] :
( ~ mem(Z,Y)
& mem(Z,X) )
| subq(X,Y) )
& ! [X,Y] :
( ! [Z] :
( mem(Z,Y)
| ~ mem(Z,X) )
| ~ subq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( ! [X,Y] :
( ( ~ mem(sK0_skl(Y,X),Y)
& mem(sK0_skl(Y,X),X) )
| subq(X,Y) )
& ! [X,Y] :
( ! [Z] :
( mem(Z,Y)
| ~ mem(Z,X) )
| ~ subq(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Z,sK0_skl(Y,X))],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( mem(X2,X1)
| ~ mem(X2,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( mem(sK0_skl(X1,X0),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( ~ mem(sK0_skl(X1,X0),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X,Y] :
( X = Y
| ~ subq(Y,X)
| ~ subq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f44,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
! [X,Y] :
( ( X != Y
| mem(X,s(Y)) )
& ( X = Y
| ~ mem(X,s(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( ! [X,Y] :
( X != Y
| mem(X,s(Y)) )
& ! [X,Y] :
( X = Y
| ~ mem(X,s(Y)) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| ~ mem(X0,s(X1)) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( X0 != X1
| mem(X0,s(X1)) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X,Y,Z] :
( ( ( ~ mem(X,Z)
& ~ mem(X,Y) )
| mem(X,u(Y,Z)) )
& ( mem(X,Z)
| mem(X,Y)
| ~ mem(X,u(Y,Z)) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f50,plain,
( ! [X,Y,Z] :
( ( ~ mem(X,Z)
& ~ mem(X,Y) )
| mem(X,u(Y,Z)) )
& ! [X,Y,Z] :
( mem(X,Z)
| mem(X,Y)
| ~ mem(X,u(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( mem(X0,X2)
| mem(X0,X1)
| ~ mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ mem(X0,X1)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ mem(X0,X2)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f59,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f60,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f169,plain,
subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f170,plain,
! [X0] : mem(X0,s(X0)),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f171,plain,
subq(a(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),a(s(s(n(e))),n(n(e)))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
inference(forward_demodulation,[status(thm)],[f59,f169]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ mem(X0,X1)
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f52]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ~ mem(X0,s(X2))
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f53]) ).
fof(f176,plain,
! [X0,X1] :
( ~ mem(X0,X1)
| mem(X0,n(X1)) ),
inference(paramodulation,[status(thm)],[f60,f174]) ).
fof(f177,plain,
! [X0,X1] : mem(X0,a(X1,X0)),
inference(resolution,[status(thm)],[f175,f170]) ).
fof(f178,plain,
! [X0] : mem(X0,n(X0)),
inference(paramodulation,[status(thm)],[f60,f177]) ).
fof(f181,plain,
! [X0,X1,X2] :
( mem(X0,s(X2))
| mem(X0,X1)
| ~ mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f51]) ).
fof(f184,plain,
! [X0,X1] :
( mem(X0,s(X1))
| mem(X0,X1)
| ~ mem(X0,n(X1)) ),
inference(paramodulation,[status(thm)],[f60,f181]) ).
fof(f186,plain,
! [X0,X1] :
( X0 = X1
| mem(X0,X1)
| ~ mem(X0,n(X1)) ),
inference(resolution,[status(thm)],[f184,f47]) ).
fof(f191,plain,
! [X0] :
( mem(X0,u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e))))))
| ~ mem(X0,a(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),a(s(s(n(e))),n(n(e))))) ),
inference(resolution,[status(thm)],[f32,f171]) ).
fof(f201,plain,
! [X0] : subq(e,X0),
inference(resolution,[status(thm)],[f33,f44]) ).
fof(f203,plain,
! [X0,X1] :
( ~ mem(sK0_skl(n(X1),X0),X1)
| subq(X0,n(X1)) ),
inference(resolution,[status(thm)],[f34,f176]) ).
fof(f204,plain,
! [X0,X1,X2] :
( ~ mem(sK0_skl(a(X1,X2),X0),X1)
| subq(X0,a(X1,X2)) ),
inference(resolution,[status(thm)],[f34,f174]) ).
fof(f210,plain,
! [X0] :
( mem(X0,a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))
| mem(X0,a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))))
| ~ mem(X0,a(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),a(s(s(n(e))),n(n(e))))) ),
inference(resolution,[status(thm)],[f191,f51]) ).
fof(f213,plain,
! [X0] :
( ~ mem(X0,u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))))
| mem(X0,a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))
| mem(X0,a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e))))) ),
inference(resolution,[status(thm)],[f210,f174]) ).
fof(f215,plain,
! [X0] :
( ~ mem(X0,n(a(n(e),n(n(e)))))
| mem(X0,a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))
| mem(X0,a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e))))) ),
inference(resolution,[status(thm)],[f213,f53]) ).
fof(f218,plain,
! [X0] :
( mem(X0,s(a(n(e),n(n(e)))))
| mem(X0,u(s(s(s(n(e)))),n(n(s(n(e))))))
| ~ mem(X0,n(a(n(e),n(n(e)))))
| mem(X0,a(s(n(n(e))),a(s(s(n(e))),n(n(e))))) ),
inference(resolution,[status(thm)],[f215,f181]) ).
fof(f220,plain,
! [X0] :
( mem(X0,s(a(s(s(n(e))),n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(a(n(e),n(n(e)))))
| mem(X0,u(s(s(s(n(e)))),n(n(s(n(e))))))
| ~ mem(X0,n(a(n(e),n(n(e))))) ),
inference(resolution,[status(thm)],[f218,f181]) ).
fof(f222,plain,
! [X0] :
( mem(X0,n(n(s(n(e)))))
| mem(X0,s(s(s(n(e)))))
| mem(X0,s(a(s(s(n(e))),n(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(a(n(e),n(n(e)))))
| ~ mem(X0,n(a(n(e),n(n(e))))) ),
inference(resolution,[status(thm)],[f220,f51]) ).
fof(f228,plain,
! [X0] :
( X0 = e
| ~ subq(X0,e) ),
inference(resolution,[status(thm)],[f201,f36]) ).
fof(f236,plain,
! [X0] :
( subq(X0,n(X0))
| subq(X0,n(X0)) ),
inference(resolution,[status(thm)],[f203,f33]) ).
fof(f246,plain,
! [X0] : subq(X0,n(X0)),
inference(duplicate_literals_removal,[status(thm)],[f236]) ).
fof(f248,plain,
! [X0] :
( n(X0) = X0
| ~ subq(n(X0),X0) ),
inference(resolution,[status(thm)],[f246,f36]) ).
fof(f249,plain,
! [X0,X1] :
( subq(X0,a(X0,X1))
| subq(X0,a(X0,X1)) ),
inference(resolution,[status(thm)],[f204,f33]) ).
fof(f260,plain,
! [X0,X1] : subq(X0,a(X0,X1)),
inference(duplicate_literals_removal,[status(thm)],[f249]) ).
fof(f464,plain,
! [X0] :
( X0 = a(s(s(n(e))),n(n(e)))
| mem(X0,n(n(s(n(e)))))
| mem(X0,s(s(s(n(e)))))
| mem(X0,s(n(n(e))))
| mem(X0,s(a(n(e),n(n(e)))))
| ~ mem(X0,n(a(n(e),n(n(e))))) ),
inference(resolution,[status(thm)],[f222,f47]) ).
fof(f476,plain,
! [X0] :
( X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e)))
| mem(X0,n(n(s(n(e)))))
| mem(X0,s(s(s(n(e)))))
| mem(X0,s(n(n(e))))
| ~ mem(X0,n(a(n(e),n(n(e))))) ),
inference(resolution,[status(thm)],[f464,f47]) ).
fof(f491,plain,
! [X0] :
( ~ mem(X0,a(n(e),n(n(e))))
| X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e)))
| mem(X0,n(n(s(n(e)))))
| mem(X0,s(s(s(n(e)))))
| mem(X0,s(n(n(e)))) ),
inference(resolution,[status(thm)],[f476,f176]) ).
fof(f512,plain,
! [X0] :
( ~ mem(X0,n(e))
| X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e)))
| mem(X0,n(n(s(n(e)))))
| mem(X0,s(s(s(n(e)))))
| mem(X0,s(n(n(e)))) ),
inference(resolution,[status(thm)],[f491,f174]) ).
fof(f530,plain,
! [X0] :
( X0 = s(s(n(e)))
| ~ mem(X0,n(e))
| X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e)))
| mem(X0,n(n(s(n(e)))))
| mem(X0,s(n(n(e)))) ),
inference(resolution,[status(thm)],[f512,f47]) ).
fof(f542,plain,
! [X0] :
( X0 = n(s(n(e)))
| mem(X0,n(s(n(e))))
| X0 = s(s(n(e)))
| ~ mem(X0,n(e))
| X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e)))
| mem(X0,s(n(n(e)))) ),
inference(resolution,[status(thm)],[f530,f186]) ).
fof(f965,plain,
! [X0] :
( X0 = n(n(e))
| X0 = n(s(n(e)))
| mem(X0,n(s(n(e))))
| X0 = s(s(n(e)))
| ~ mem(X0,n(e))
| X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[f542,f47]) ).
fof(f979,plain,
! [X0] :
( X0 = s(n(e))
| mem(X0,s(n(e)))
| X0 = n(n(e))
| X0 = n(s(n(e)))
| X0 = s(s(n(e)))
| ~ mem(X0,n(e))
| X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[f965,f186]) ).
fof(f1243,plain,
! [X0] :
( X0 = n(e)
| X0 = s(n(e))
| X0 = n(n(e))
| X0 = n(s(n(e)))
| X0 = s(s(n(e)))
| ~ mem(X0,n(e))
| X0 = a(n(e),n(n(e)))
| X0 = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[f979,f47]) ).
fof(f1268,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| e = n(s(n(e)))
| e = s(s(n(e)))
| e = a(n(e),n(n(e)))
| e = a(s(s(n(e))),n(n(e))) ),
inference(resolution,[status(thm)],[f1243,f178]) ).
fof(f1339,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| e = n(s(n(e)))
| e = s(s(n(e)))
| e = a(n(e),n(n(e)))
| subq(s(s(n(e))),e) ),
inference(paramodulation,[status(thm)],[f1268,f260]) ).
fof(f1347,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| e = n(s(n(e)))
| e = s(s(n(e)))
| e = a(n(e),n(n(e))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1339,f228]) ).
fof(f1371,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| e = n(s(n(e)))
| e = s(s(n(e)))
| subq(n(e),e) ),
inference(paramodulation,[status(thm)],[f1347,f260]) ).
fof(f1379,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| e = n(s(n(e)))
| e = s(s(n(e))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1371,f248]) ).
fof(f1431,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| e = n(s(n(e)))
| mem(s(n(e)),e) ),
inference(paramodulation,[status(thm)],[f1379,f170]) ).
fof(f1434,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| e = n(s(n(e))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1431,f44]) ).
fof(f1456,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e))
| subq(s(n(e)),e) ),
inference(paramodulation,[status(thm)],[f1434,f246]) ).
fof(f1466,plain,
( e = n(e)
| e = s(n(e))
| e = n(n(e)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1456,f228]) ).
fof(f1834,plain,
( e = n(e)
| e = n(n(e))
| mem(n(e),e) ),
inference(paramodulation,[status(thm)],[f1466,f170]) ).
fof(f1840,plain,
( e = n(e)
| e = n(n(e)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1834,f44]) ).
fof(f1893,plain,
( e = n(e)
| subq(n(e),e) ),
inference(paramodulation,[status(thm)],[f1840,f246]) ).
fof(f2175,plain,
e = n(e),
inference(forward_subsumption_resolution,[status(thm)],[f1893,f248]) ).
fof(f8492,plain,
mem(e,e),
inference(paramodulation,[status(thm)],[f2175,f178]) ).
fof(f8575,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8492,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV572+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 07:30:13 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 47.94/6.88 % Refutation found
% 47.94/6.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 47.94/6.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 46.00/7.00 % Elapsed time: 6.563122 seconds
% 46.00/7.00 % CPU time: 51.274636 seconds
% 46.00/7.00 % Total memory used: 390.475 MB
% 46.00/7.00 % Net memory used: 361.241 MB
%------------------------------------------------------------------------------