%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV542+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 : n020.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 02:33:00 PM UTC 2026
% Result : Theorem 127.24s 16.61s
% Output : CNFRefutation 93.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 151 ( 33 unt; 0 def)
% Number of atoms : 391 ( 29 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 390 ( 150 ~; 183 |; 44 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 318 ( 307 !; 11 ?)
% 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(f3,axiom,
! [X,Y] :
( disj(X,Y)
<=> ~ ? [Z] :
( mem(Z,Y)
& mem(Z,X) ) ),
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(f7,axiom,
! [X,Y,Z] :
( mem(X,m(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(f10,axiom,
! [X,Y] :
( mem(X,p(Y))
<=> subq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( atleast2p(X)
<=> ? [Y] :
( ~ subq(X,p(Y))
& mem(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( atleast3p(X)
<=> ? [Y] :
( ~ subq(X,Y)
& atleast2p(Y)
& subq(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ atleast3p(a(p(s(s(n(e)))),n(s(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(f37,plain,
! [X,Y] :
( disj(X,Y)
<=> ! [Z] :
( ~ mem(Z,Y)
| ~ mem(Z,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [X,Y] :
( ( ? [Z] :
( mem(Z,Y)
& mem(Z,X) )
| disj(X,Y) )
& ( ! [Z] :
( ~ mem(Z,Y)
| ~ mem(Z,X) )
| ~ disj(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [X,Y] :
( ? [Z] :
( mem(Z,Y)
& mem(Z,X) )
| disj(X,Y) )
& ! [X,Y] :
( ! [Z] :
( ~ mem(Z,Y)
| ~ mem(Z,X) )
| ~ disj(X,Y) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [X,Y] :
( ( mem(sK1_skl(Y,X),Y)
& mem(sK1_skl(Y,X),X) )
| disj(X,Y) )
& ! [X,Y] :
( ! [Z] :
( ~ mem(Z,Y)
| ~ mem(Z,X) )
| ~ disj(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Z,sK1_skl(Y,X))],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ mem(X2,X1)
| ~ mem(X2,X0)
| ~ disj(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( mem(sK1_skl(X1,X0),X0)
| disj(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( mem(sK1_skl(X1,X0),X1)
| disj(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
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(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(f54,plain,
! [X,Y,Z] :
( ( mem(X,Z)
| ~ mem(X,Y)
| mem(X,m(Y,Z)) )
& ( ( ~ mem(X,Z)
& mem(X,Y) )
| ~ mem(X,m(Y,Z)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f55,plain,
( ! [X,Y,Z] :
( mem(X,Z)
| ~ mem(X,Y)
| mem(X,m(Y,Z)) )
& ! [X,Y,Z] :
( ( ~ mem(X,Z)
& mem(X,Y) )
| ~ mem(X,m(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( mem(X0,X1)
| ~ mem(X0,m(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ mem(X0,X2)
| ~ mem(X0,m(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
! [X0,X1,X2] :
( mem(X0,X2)
| ~ mem(X0,X1)
| mem(X0,m(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
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(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(f63,plain,
! [X0,X1] :
( subq(X0,X1)
| ~ mem(X0,p(X1)) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| mem(X0,p(X1)) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
! [X] :
( ( ! [Y] :
( subq(X,p(Y))
| ~ mem(Y,X) )
| atleast2p(X) )
& ( ? [Y] :
( ~ subq(X,p(Y))
& mem(Y,X) )
| ~ atleast2p(X) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( ! [X] :
( ! [Y] :
( subq(X,p(Y))
| ~ mem(Y,X) )
| atleast2p(X) )
& ! [X] :
( ? [Y] :
( ~ subq(X,p(Y))
& mem(Y,X) )
| ~ atleast2p(X) ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
( ! [X] :
( ! [Y] :
( subq(X,p(Y))
| ~ mem(Y,X) )
| atleast2p(X) )
& ! [X] :
( ( ~ subq(X,p(sK2_skl(X)))
& mem(sK2_skl(X),X) )
| ~ atleast2p(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(Y,sK2_skl(X))],[f66]) ).
fof(f69,plain,
! [X0] :
( ~ subq(X0,p(sK2_skl(X0)))
| ~ atleast2p(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
! [X0,X1] :
( subq(X0,p(X1))
| ~ mem(X1,X0)
| atleast2p(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [X] :
( ( ! [Y] :
( subq(X,Y)
| ~ atleast2p(Y)
| ~ subq(Y,X) )
| atleast3p(X) )
& ( ? [Y] :
( ~ subq(X,Y)
& atleast2p(Y)
& subq(Y,X) )
| ~ atleast3p(X) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f72,plain,
( ! [X] :
( ! [Y] :
( subq(X,Y)
| ~ atleast2p(Y)
| ~ subq(Y,X) )
| atleast3p(X) )
& ! [X] :
( ? [Y] :
( ~ subq(X,Y)
& atleast2p(Y)
& subq(Y,X) )
| ~ atleast3p(X) ) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
( ! [X] :
( ! [Y] :
( subq(X,Y)
| ~ atleast2p(Y)
| ~ subq(Y,X) )
| atleast3p(X) )
& ! [X] :
( ( ~ subq(X,sK3_skl(X))
& atleast2p(sK3_skl(X))
& subq(sK3_skl(X),X) )
| ~ atleast3p(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(Y,sK3_skl(X))],[f72]) ).
fof(f77,plain,
! [X0,X1] :
( subq(X0,X1)
| ~ atleast2p(X1)
| ~ subq(X1,X0)
| atleast3p(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f169,plain,
~ atleast3p(a(p(s(s(n(e)))),n(s(n(e))))),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f170,plain,
! [X0] : mem(X0,s(X0)),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f173,plain,
! [X0,X1,X2] :
( ~ subq(X2,X0)
| mem(X2,X1)
| ~ subq(p(X0),X1) ),
inference(resolution,[status(thm)],[f32,f64]) ).
fof(f174,plain,
! [X0,X1] :
( mem(X0,X1)
| ~ subq(s(X0),X1) ),
inference(resolution,[status(thm)],[f32,f170]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ~ mem(X1,p(X2))
| atleast2p(p(X2))
| ~ subq(X0,X2)
| mem(X0,p(X1)) ),
inference(resolution,[status(thm)],[f173,f70]) ).
fof(f180,plain,
! [X0,X1] :
( subq(sK0_skl(X1,p(X0)),X0)
| subq(p(X0),X1) ),
inference(resolution,[status(thm)],[f33,f63]) ).
fof(f181,plain,
! [X0,X1] :
( sK0_skl(X1,s(X0)) = X0
| subq(s(X0),X1) ),
inference(resolution,[status(thm)],[f33,f47]) ).
fof(f182,plain,
! [X0] : subq(e,X0),
inference(resolution,[status(thm)],[f33,f44]) ).
fof(f184,plain,
! [X0] :
( subq(X0,X0)
| subq(X0,X0) ),
inference(resolution,[status(thm)],[f34,f33]) ).
fof(f185,plain,
! [X0,X1] :
( ~ subq(sK0_skl(p(X1),X0),X1)
| subq(X0,p(X1)) ),
inference(resolution,[status(thm)],[f34,f64]) ).
fof(f186,plain,
! [X0] : subq(X0,X0),
inference(duplicate_literals_removal,[status(thm)],[f184]) ).
fof(f193,plain,
! [X0,X1] :
( ~ mem(X0,X1)
| atleast2p(X1)
| p(X0) = X1
| ~ subq(p(X0),X1) ),
inference(resolution,[status(thm)],[f36,f70]) ).
fof(f200,plain,
! [X0] :
( X0 = e
| ~ subq(X0,e) ),
inference(resolution,[status(thm)],[f182,f36]) ).
fof(f201,plain,
! [X0,X1] :
( ~ mem(X1,s(X0))
| atleast2p(s(X0))
| mem(X0,p(X1)) ),
inference(resolution,[status(thm)],[f174,f70]) ).
fof(f224,plain,
! [X0] :
( sK0_skl(X0,p(e)) = e
| subq(p(e),X0) ),
inference(resolution,[status(thm)],[f180,f200]) ).
fof(f228,plain,
! [X0,X1] :
( subq(s(X0),p(X1))
| ~ subq(X0,X1)
| subq(s(X0),p(X1)) ),
inference(paramodulation,[status(thm)],[f181,f185]) ).
fof(f230,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| subq(s(X0),p(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f228]) ).
fof(f257,plain,
! [X0,X1] :
( subq(sK1_skl(X1,p(X0)),X0)
| disj(p(X0),X1) ),
inference(resolution,[status(thm)],[f42,f63]) ).
fof(f262,plain,
! [X0,X1] :
( sK1_skl(s(X1),X0) = X1
| disj(X0,s(X1)) ),
inference(resolution,[status(thm)],[f43,f47]) ).
fof(f287,plain,
! [X0,X1] :
( disj(p(X0),s(X1))
| subq(X1,X0)
| disj(p(X0),s(X1)) ),
inference(paramodulation,[status(thm)],[f262,f257]) ).
fof(f288,plain,
! [X0,X1] :
( subq(X1,X0)
| disj(p(X0),s(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f287]) ).
fof(f306,plain,
! [X0,X1,X2] :
( ~ mem(X0,X1)
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f52]) ).
fof(f307,plain,
! [X0,X1,X2] :
( subq(X2,u(X0,X1))
| ~ mem(sK0_skl(u(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f53,f34]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ mem(X0,s(X2))
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f53]) ).
fof(f311,plain,
! [X0,X1,X2] :
( disj(m(X1,X2),X0)
| mem(sK1_skl(X0,m(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f56,f42]) ).
fof(f312,plain,
! [X0,X1,X2] :
( subq(m(X1,X2),X0)
| mem(sK0_skl(X0,m(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f56,f33]) ).
fof(f314,plain,
! [X0,X1,X2] :
( disj(X2,m(X0,X1))
| ~ mem(sK1_skl(m(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f57,f43]) ).
fof(f318,plain,
! [X0] :
( ~ subq(X0,sK2_skl(s(X0)))
| ~ atleast2p(s(X0)) ),
inference(resolution,[status(thm)],[f69,f230]) ).
fof(f322,plain,
! [X0,X1,X2] :
( subq(X2,a(X0,X1))
| ~ mem(sK0_skl(a(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f306,f34]) ).
fof(f324,plain,
! [X0,X1] :
( ~ mem(X0,X1)
| mem(X0,n(X1)) ),
inference(paramodulation,[status(thm)],[f60,f306]) ).
fof(f372,plain,
! [X0,X1] :
( subq(X1,n(X0))
| ~ mem(sK0_skl(n(X0),X1),X0) ),
inference(resolution,[status(thm)],[f324,f34]) ).
fof(f374,plain,
! [X0,X1,X2] :
( ~ mem(X2,s(X0))
| ~ mem(X2,p(X1))
| subq(X0,X1) ),
inference(resolution,[status(thm)],[f288,f41]) ).
fof(f378,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| mem(X0,n(X1)) ),
inference(paramodulation,[status(thm)],[f60,f309]) ).
fof(f383,plain,
! [X0] : mem(X0,n(X0)),
inference(resolution,[status(thm)],[f378,f170]) ).
fof(f384,plain,
! [X0,X1] :
( mem(X0,X1)
| ~ subq(n(X0),X1) ),
inference(resolution,[status(thm)],[f383,f32]) ).
fof(f388,plain,
~ atleast2p(s(e)),
inference(resolution,[status(thm)],[f318,f182]) ).
fof(f616,plain,
! [X0] :
( subq(X0,n(X0))
| subq(X0,n(X0)) ),
inference(resolution,[status(thm)],[f372,f33]) ).
fof(f625,plain,
! [X0] : subq(X0,n(X0)),
inference(duplicate_literals_removal,[status(thm)],[f616]) ).
fof(f630,plain,
! [X0] : mem(X0,n(s(X0))),
inference(resolution,[status(thm)],[f625,f174]) ).
fof(f668,plain,
! [X0,X1] :
( mem(X0,X1)
| ~ subq(n(s(X0)),X1) ),
inference(resolution,[status(thm)],[f630,f32]) ).
fof(f2288,plain,
! [X0] :
( atleast2p(s(X0))
| mem(X0,p(X0)) ),
inference(resolution,[status(thm)],[f201,f170]) ).
fof(f2388,plain,
! [X0,X1] :
( mem(X0,X1)
| ~ subq(p(X0),X1)
| atleast2p(s(X0)) ),
inference(resolution,[status(thm)],[f2288,f32]) ).
fof(f2686,plain,
! [X0] :
( subq(p(e),p(X0))
| ~ subq(e,X0)
| subq(p(e),p(X0)) ),
inference(paramodulation,[status(thm)],[f224,f185]) ).
fof(f2690,plain,
! [X0] :
( subq(p(e),X0)
| ~ mem(e,X0)
| subq(p(e),X0) ),
inference(paramodulation,[status(thm)],[f224,f34]) ).
fof(f2694,plain,
! [X0] :
( ~ subq(e,X0)
| subq(p(e),p(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f2686]) ).
fof(f2695,plain,
! [X0] : subq(p(e),p(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f2694,f182]) ).
fof(f2699,plain,
! [X0] :
( ~ mem(e,X0)
| subq(p(e),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2690]) ).
fof(f2701,plain,
! [X0] :
( mem(e,p(X0))
| atleast2p(s(e)) ),
inference(resolution,[status(thm)],[f2695,f2388]) ).
fof(f2721,plain,
! [X0] : mem(e,p(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f2701,f388]) ).
fof(f2727,plain,
! [X0,X1] :
( atleast2p(p(X1))
| ~ subq(X0,X1)
| mem(X0,p(e)) ),
inference(resolution,[status(thm)],[f2721,f175]) ).
fof(f2779,plain,
! [X0,X1] :
( subq(X0,a(X0,X1))
| subq(X0,a(X0,X1)) ),
inference(resolution,[status(thm)],[f322,f33]) ).
fof(f2797,plain,
! [X0,X1] : subq(X0,a(X0,X1)),
inference(duplicate_literals_removal,[status(thm)],[f2779]) ).
fof(f2831,plain,
! [X0,X1] :
( subq(a(X0,X1),X0)
| ~ atleast2p(X0)
| atleast3p(a(X0,X1)) ),
inference(resolution,[status(thm)],[f2797,f77]) ).
fof(f2873,plain,
! [X0,X1] :
( subq(X0,u(X1,X0))
| subq(X0,u(X1,X0)) ),
inference(resolution,[status(thm)],[f307,f33]) ).
fof(f2891,plain,
! [X0,X1] : subq(X0,u(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f2873]) ).
fof(f2943,plain,
! [X0] :
( ~ mem(e,X0)
| atleast2p(X0)
| p(e) = X0
| ~ mem(e,X0) ),
inference(resolution,[status(thm)],[f2699,f193]) ).
fof(f2991,plain,
! [X0] :
( atleast2p(X0)
| p(e) = X0
| ~ mem(e,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2943]) ).
fof(f3254,plain,
! [X0,X1] : mem(X0,u(X1,s(X0))),
inference(resolution,[status(thm)],[f2891,f174]) ).
fof(f3277,plain,
! [X0,X1] : mem(X0,a(X1,X0)),
inference(forward_demodulation,[status(thm)],[f59,f3254]) ).
fof(f3279,plain,
! [X0,X1,X2] :
( mem(X1,X2)
| ~ subq(a(X0,X1),X2) ),
inference(resolution,[status(thm)],[f3277,f32]) ).
fof(f3493,plain,
! [X0,X1] :
( subq(m(X0,X1),X0)
| subq(m(X0,X1),X0) ),
inference(resolution,[status(thm)],[f312,f34]) ).
fof(f3514,plain,
! [X0,X1] : subq(m(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f3493]) ).
fof(f3531,plain,
! [X0,X1,X2] :
( disj(m(X0,X1),m(X2,X0))
| disj(m(X0,X1),m(X2,X0)) ),
inference(resolution,[status(thm)],[f314,f311]) ).
fof(f3551,plain,
! [X0,X1,X2] : disj(m(X0,X1),m(X2,X0)),
inference(duplicate_literals_removal,[status(thm)],[f3531]) ).
fof(f3722,plain,
! [X0,X1] :
( X0 = m(X0,X1)
| ~ subq(X0,m(X0,X1)) ),
inference(resolution,[status(thm)],[f3514,f36]) ).
fof(f3784,plain,
! [X0,X1,X2,X3] :
( ~ mem(X0,m(X3,X1))
| ~ mem(X0,m(X1,X2)) ),
inference(resolution,[status(thm)],[f3551,f41]) ).
fof(f4436,plain,
( atleast2p(s(e))
| p(e) = s(e) ),
inference(resolution,[status(thm)],[f2991,f170]) ).
fof(f4442,plain,
p(e) = s(e),
inference(forward_subsumption_resolution,[status(thm)],[f4436,f388]) ).
fof(f4508,plain,
! [X0] :
( subq(X0,e)
| ~ mem(X0,s(e)) ),
inference(paramodulation,[status(thm)],[f4442,f63]) ).
fof(f14647,plain,
! [X0,X1] :
( ~ mem(e,s(X0))
| subq(X0,X1) ),
inference(resolution,[status(thm)],[f374,f2721]) ).
fof(f16395,plain,
! [X0,X1] :
( atleast2p(p(X1))
| ~ subq(X0,X1)
| mem(X0,s(e)) ),
inference(forward_demodulation,[status(thm)],[f4442,f2727]) ).
fof(f16411,plain,
! [X0,X1] :
( subq(X0,e)
| atleast2p(p(X1))
| ~ subq(X0,X1) ),
inference(resolution,[status(thm)],[f16395,f4508]) ).
fof(f16420,plain,
! [X0,X1] :
( X0 = e
| atleast2p(p(X1))
| ~ subq(X0,X1) ),
inference(resolution,[status(thm)],[f16395,f47]) ).
fof(f16445,plain,
! [X0,X1] :
( m(X0,X1) = e
| atleast2p(p(X0)) ),
inference(resolution,[status(thm)],[f16420,f3514]) ).
fof(f16594,plain,
! [X0,X1] :
( atleast2p(p(X0))
| X0 = m(X0,X1)
| ~ subq(X0,e) ),
inference(paramodulation,[status(thm)],[f16445,f3722]) ).
fof(f16619,plain,
! [X0,X1,X2] :
( atleast2p(p(X1))
| mem(X0,X2)
| ~ mem(X0,X1)
| mem(X0,e) ),
inference(paramodulation,[status(thm)],[f16445,f58]) ).
fof(f16627,plain,
! [X0,X1,X2] :
( atleast2p(p(X1))
| mem(X0,X2)
| ~ mem(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f16619,f44]) ).
fof(f18193,plain,
! [X0] :
( subq(X0,e)
| atleast2p(p(X0)) ),
inference(resolution,[status(thm)],[f16411,f186]) ).
fof(f19723,plain,
! [X0,X1] :
( atleast2p(p(X0))
| X0 = m(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f16594,f18193]) ).
fof(f19787,plain,
! [X0,X1,X2,X3] :
( atleast2p(p(X3))
| ~ mem(X0,X3)
| ~ mem(X0,m(X1,X2)) ),
inference(paramodulation,[status(thm)],[f19723,f3784]) ).
fof(f19846,plain,
! [X0,X1] :
( atleast2p(p(X1))
| ~ mem(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f19787,f16627]) ).
fof(f20188,plain,
! [X0] : atleast2p(p(s(X0))),
inference(resolution,[status(thm)],[f19846,f170]) ).
fof(f25590,plain,
! [X0,X1] :
( mem(X1,X0)
| ~ atleast2p(X0)
| atleast3p(a(X0,X1)) ),
inference(resolution,[status(thm)],[f2831,f3279]) ).
fof(f25641,plain,
( mem(n(s(n(e))),p(s(s(n(e)))))
| ~ atleast2p(p(s(s(n(e))))) ),
inference(resolution,[status(thm)],[f25590,f169]) ).
fof(f25647,plain,
mem(n(s(n(e))),p(s(s(n(e))))),
inference(forward_subsumption_resolution,[status(thm)],[f25641,f20188]) ).
fof(f26557,plain,
subq(n(s(n(e))),s(s(n(e)))),
inference(resolution,[status(thm)],[f25647,f63]) ).
fof(f26590,plain,
mem(n(e),s(s(n(e)))),
inference(resolution,[status(thm)],[f26557,f668]) ).
fof(f26639,plain,
n(e) = s(n(e)),
inference(resolution,[status(thm)],[f26590,f47]) ).
fof(f26698,plain,
! [X0] :
( ~ mem(e,n(e))
| subq(n(e),X0) ),
inference(paramodulation,[status(thm)],[f26639,f14647]) ).
fof(f26869,plain,
! [X0] : subq(n(e),X0),
inference(forward_subsumption_resolution,[status(thm)],[f26698,f383]) ).
fof(f26921,plain,
! [X0] : mem(e,X0),
inference(resolution,[status(thm)],[f26869,f384]) ).
fof(f27041,plain,
$false,
inference(resolution,[status(thm)],[f26921,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV542+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 07:27:03 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 127.24/16.61 % Refutation found
% 127.24/16.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 127.24/16.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 93.37/16.71 % Elapsed time: 16.344984 seconds
% 93.37/16.71 % CPU time: 128.402162 seconds
% 93.37/16.71 % Total memory used: 474.170 MB
% 93.37/16.71 % Net memory used: 410.069 MB
%------------------------------------------------------------------------------