%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV582+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 : n019.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 02:33:03 PM UTC 2026
% Result : Theorem 194.69s 25.13s
% Output : CNFRefutation 194.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 98 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 36 ~; 42 |; 10 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 84 ( 82 !; 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(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(f26,conjecture,
subq(u(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(s(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ subq(u(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(s(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(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(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(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(f169,plain,
~ subq(u(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(s(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e)))))),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f174,plain,
! [X0,X1,X2] :
( mem(sK0_skl(X2,u(X0,X1)),X1)
| mem(sK0_skl(X2,u(X0,X1)),X0)
| subq(u(X0,X1),X2) ),
inference(resolution,[status(thm)],[f33,f51]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ mem(sK0_skl(u(X1,X2),X0),X2)
| subq(X0,u(X1,X2)) ),
inference(resolution,[status(thm)],[f34,f53]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ~ mem(sK0_skl(u(X1,X2),X0),X1)
| subq(X0,u(X1,X2)) ),
inference(resolution,[status(thm)],[f34,f52]) ).
fof(f185,plain,
~ subq(a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e)))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e)))))),
inference(backward_demodulation,[status(thm)],[f59,f169]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ~ mem(X0,s(X2))
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f53]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ mem(X0,X1)
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f52]) ).
fof(f188,plain,
! [X0,X1,X2] :
( mem(X0,s(X2))
| mem(X0,X1)
| ~ mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f51]) ).
fof(f196,plain,
! [X0,X1,X2] :
( mem(sK0_skl(X2,u(X0,s(X1))),s(X1))
| mem(sK0_skl(X2,u(X0,s(X1))),X0)
| subq(a(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f59,f174]) ).
fof(f197,plain,
! [X0,X1,X2] :
( mem(sK0_skl(X2,u(X0,s(X1))),s(X1))
| mem(sK0_skl(X2,a(X0,X1)),X0)
| subq(a(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f59,f196]) ).
fof(f198,plain,
! [X0,X1,X2] :
( mem(sK0_skl(X2,a(X0,X1)),s(X1))
| mem(sK0_skl(X2,a(X0,X1)),X0)
| subq(a(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f59,f197]) ).
fof(f221,plain,
~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),
inference(resolution,[status(thm)],[f178,f185]) ).
fof(f227,plain,
~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),s(n(e))),
inference(resolution,[status(thm)],[f221,f187]) ).
fof(f231,plain,
~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e)))))),
inference(resolution,[status(thm)],[f179,f185]) ).
fof(f257,plain,
~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),
inference(resolution,[status(thm)],[f231,f53]) ).
fof(f258,plain,
~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),s(u(n(e),n(s(n(e)))))),
inference(resolution,[status(thm)],[f231,f52]) ).
fof(f259,plain,
~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),s(s(s(n(e))))),
inference(resolution,[status(thm)],[f257,f187]) ).
fof(f298,plain,
! [X0] :
( mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),X0)
| ~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(X0,s(s(n(e))))) ),
inference(resolution,[status(thm)],[f259,f188]) ).
fof(f299,plain,
! [X0] :
( mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),X0)
| ~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(X0,u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[f258,f188]) ).
fof(f307,plain,
! [X0,X1,X2,X3] :
( mem(sK0_skl(X2,a(X0,X1)),a(X3,X1))
| mem(sK0_skl(X2,a(X0,X1)),X0)
| subq(a(X0,X1),X2) ),
inference(resolution,[status(thm)],[f198,f186]) ).
fof(f2235,plain,
! [X0] :
( mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(X0,s(n(n(e)))))
| mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[f307,f185]) ).
fof(f2716,plain,
mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e)))))),
inference(resolution,[status(thm)],[f2235,f257]) ).
fof(f2924,plain,
mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),a(s(n(e)),s(s(n(e))))),
inference(resolution,[status(thm)],[f2716,f299]) ).
fof(f3172,plain,
mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e))))),a(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(n(n(e))))),s(n(e))),
inference(resolution,[status(thm)],[f2924,f298]) ).
fof(f3189,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3172,f227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV582+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:28:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 194.69/25.13 % Refutation found
% 194.69/25.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 194.69/25.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.77/25.63 % Elapsed time: 25.259811 seconds
% 12.77/25.63 % CPU time: 196.572463 seconds
% 12.77/25.63 % Total memory used: 598.766 MB
% 12.77/25.63 % Net memory used: 521.239 MB
%------------------------------------------------------------------------------