%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV580+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 : n016.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 19.76s 2.96s
% Output : CNFRefutation 19.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 24 unt; 0 def)
% Number of atoms : 177 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 156 ( 58 ~; 76 |; 14 &)
% ( 5 <=>; 3 =>; 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 : 140 ( 138 !; 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(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(f10,axiom,
! [X,Y] :
( mem(X,p(Y))
<=> subq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
subq(u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ subq(u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(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(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(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(f61,plain,
! [X,Y] :
( ( ~ subq(X,Y)
| mem(X,p(Y)) )
& ( subq(X,Y)
| ~ mem(X,p(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f62,plain,
( ! [X,Y] :
( ~ subq(X,Y)
| mem(X,p(Y)) )
& ! [X,Y] :
( subq(X,Y)
| ~ mem(X,p(Y)) ) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| mem(X0,p(X1)) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f169,plain,
~ subq(u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f173,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(f177,plain,
! [X0] :
( subq(X0,X0)
| subq(X0,X0) ),
inference(resolution,[status(thm)],[f34,f33]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ mem(sK0_skl(u(X1,X2),X0),X1)
| subq(X0,u(X1,X2)) ),
inference(resolution,[status(thm)],[f34,f52]) ).
fof(f179,plain,
! [X0] : subq(X0,X0),
inference(duplicate_literals_removal,[status(thm)],[f177]) ).
fof(f184,plain,
! [X0,X1,X2] :
( subq(X2,u(X0,X1))
| ~ mem(sK0_skl(u(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f53,f34]) ).
fof(f193,plain,
( mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),s(n(n(n(e)))))
| mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e))))))) ),
inference(resolution,[status(thm)],[f173,f169]) ).
fof(f197,plain,
! [X0,X1,X2] :
( X0 = u(X1,X2)
| ~ subq(X0,u(X1,X2))
| mem(sK0_skl(X0,u(X1,X2)),X2)
| mem(sK0_skl(X0,u(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f173,f36]) ).
fof(f204,plain,
! [X0] : mem(X0,p(X0)),
inference(resolution,[status(thm)],[f179,f64]) ).
fof(f221,plain,
! [X0,X1] :
( subq(X0,u(X0,X1))
| subq(X0,u(X0,X1)) ),
inference(resolution,[status(thm)],[f178,f33]) ).
fof(f224,plain,
! [X0,X1] : subq(X0,u(X0,X1)),
inference(duplicate_literals_removal,[status(thm)],[f221]) ).
fof(f225,plain,
~ mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),s(n(n(n(e))))),
inference(resolution,[status(thm)],[f184,f169]) ).
fof(f235,plain,
! [X0,X1] :
( u(X0,X1) = X0
| ~ subq(u(X0,X1),X0) ),
inference(resolution,[status(thm)],[f224,f36]) ).
fof(f242,plain,
mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e))))))),
inference(backward_subsumption_resolution,[status(thm)],[f193,f225]) ).
fof(f243,plain,
( mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),u(s(s(s(n(e)))),n(s(n(n(e))))))
| mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),s(u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[f242,f51]) ).
fof(f281,plain,
~ subq(u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),
inference(backward_demodulation,[status(thm)],[f59,f169]) ).
fof(f284,plain,
! [X0,X1] : subq(X0,a(X0,X1)),
inference(paramodulation,[status(thm)],[f59,f224]) ).
fof(f285,plain,
! [X0,X1,X2] :
( subq(X2,a(X0,X1))
| ~ mem(sK0_skl(u(X0,s(X1)),X2),s(X1)) ),
inference(paramodulation,[status(thm)],[f59,f184]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ~ mem(sK0_skl(a(X1,X2),X0),X1)
| subq(X0,u(X1,s(X2))) ),
inference(paramodulation,[status(thm)],[f59,f178]) ).
fof(f298,plain,
~ subq(a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),
inference(forward_demodulation,[status(thm)],[f59,f281]) ).
fof(f301,plain,
! [X0,X1,X2] :
( subq(X2,a(X0,X1))
| ~ mem(sK0_skl(a(X0,X1),X2),s(X1)) ),
inference(forward_demodulation,[status(thm)],[f59,f285]) ).
fof(f302,plain,
! [X0,X1,X2] :
( ~ mem(sK0_skl(a(X1,X2),X0),X1)
| subq(X0,a(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f59,f286]) ).
fof(f314,plain,
! [X0,X1] :
( a(X0,X1) = X0
| ~ subq(a(X0,X1),X0) ),
inference(resolution,[status(thm)],[f284,f36]) ).
fof(f347,plain,
( mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),u(s(s(s(n(e)))),n(s(n(n(e))))))
| mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),s(u(n(e),n(s(n(e)))))) ),
inference(forward_demodulation,[status(thm)],[f59,f243]) ).
fof(f348,plain,
( mem(sK0_skl(u(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),u(s(s(s(n(e)))),n(s(n(n(e))))))
| mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(u(n(e),n(s(n(e)))))) ),
inference(forward_demodulation,[status(thm)],[f59,f347]) ).
fof(f349,plain,
( mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),u(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),s(n(n(n(e)))))),u(s(s(s(n(e)))),n(s(n(n(e))))))
| mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(u(n(e),n(s(n(e)))))) ),
inference(forward_demodulation,[status(thm)],[f59,f348]) ).
fof(f350,plain,
( mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e))))))
| mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(u(n(e),n(s(n(e)))))) ),
inference(forward_demodulation,[status(thm)],[f59,f349]) ).
fof(f352,plain,
( mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),n(s(n(n(e)))))
| mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(s(s(n(e)))))
| mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[f350,f51]) ).
fof(f407,plain,
! [X0,X1] :
( X0 = u(X0,X1)
| mem(sK0_skl(X0,u(X0,X1)),X1)
| mem(sK0_skl(X0,u(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f197,f224]) ).
fof(f831,plain,
! [X0,X1] :
( subq(s(X0),a(X1,X0))
| subq(s(X0),a(X1,X0)) ),
inference(resolution,[status(thm)],[f301,f33]) ).
fof(f837,plain,
! [X0,X1] : subq(s(X0),a(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f831]) ).
fof(f928,plain,
~ mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e))))))),
inference(resolution,[status(thm)],[f302,f298]) ).
fof(f967,plain,
~ mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),
inference(resolution,[status(thm)],[f928,f53]) ).
fof(f968,plain,
~ mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(u(n(e),n(s(n(e)))))),
inference(resolution,[status(thm)],[f928,f52]) ).
fof(f972,plain,
( mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),n(s(n(n(e)))))
| mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(s(s(n(e))))) ),
inference(backward_subsumption_resolution,[status(thm)],[f352,f968]) ).
fof(f1066,plain,
~ mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),n(s(n(n(e))))),
inference(resolution,[status(thm)],[f967,f53]) ).
fof(f1067,plain,
~ mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),p(s(s(n(e))))),
inference(resolution,[status(thm)],[f967,f52]) ).
fof(f1364,plain,
mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),s(s(s(n(e))))),
inference(forward_subsumption_resolution,[status(thm)],[f972,f1066]) ).
fof(f6131,plain,
! [X0,X1] :
( subq(u(X0,X1),X0)
| X0 = u(X0,X1)
| mem(sK0_skl(X0,u(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f407,f34]) ).
fof(f6179,plain,
! [X0,X1] :
( X0 = u(X0,X1)
| mem(sK0_skl(X0,u(X0,X1)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f6131,f235]) ).
fof(f6460,plain,
! [X0,X1] :
( sK0_skl(X0,u(X0,s(X1))) = X1
| X0 = u(X0,s(X1)) ),
inference(resolution,[status(thm)],[f6179,f47]) ).
fof(f6504,plain,
! [X0,X1] :
( sK0_skl(X0,u(X0,s(X1))) = X1
| X0 = a(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f59,f6460]) ).
fof(f6505,plain,
! [X0,X1] :
( sK0_skl(X0,a(X0,X1)) = X1
| X0 = a(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f59,f6504]) ).
fof(f7946,plain,
! [X0,X1] :
( X0 = a(X0,X1)
| ~ mem(X1,X0)
| subq(a(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f6505,f34]) ).
fof(f7953,plain,
! [X0,X1] :
( X1 = a(X1,X0)
| ~ mem(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f7946,f314]) ).
fof(f8032,plain,
! [X0] : p(X0) = a(p(X0),X0),
inference(resolution,[status(thm)],[f7953,f204]) ).
fof(f8102,plain,
! [X0] : subq(s(X0),p(X0)),
inference(paramodulation,[status(thm)],[f8032,f837]) ).
fof(f8140,plain,
! [X0,X1] :
( mem(X0,p(X1))
| ~ mem(X0,s(X1)) ),
inference(resolution,[status(thm)],[f8102,f32]) ).
fof(f8754,plain,
mem(sK0_skl(a(u(s(u(n(e),n(s(n(e))))),u(p(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e)))),a(u(s(u(n(e),n(s(n(e))))),u(s(s(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),p(s(s(n(e))))),
inference(resolution,[status(thm)],[f8140,f1364]) ).
fof(f8785,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8754,f1067]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV580+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 07:32:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 19.76/2.96 % Refutation found
% 19.76/2.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.76/2.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.95/3.02 % Elapsed time: 2.631285 seconds
% 3.95/3.02 % CPU time: 20.547870 seconds
% 3.95/3.02 % Total memory used: 313.116 MB
% 3.95/3.02 % Net memory used: 280.749 MB
%------------------------------------------------------------------------------