%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV571+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 : n011.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 113.28s 14.84s
% Output : CNFRefutation 106.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 121 ( 21 unt; 11 def)
% Number of atoms : 310 ( 79 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 301 ( 112 ~; 153 |; 17 &)
% ( 16 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 132 ( 130 !; 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(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(f26,conjecture,
~ subq(u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(n(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(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(n(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,X0)
| mem(X2,X1)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( subq(X1,X0)
| mem(sK0_skl(X0,X1),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,u(X2,X1))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
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(f57,plain,
! [X0,X1,X2] :
( ~ mem(X0,X2)
| ~ mem(X0,m(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
! [X0,X1] : u(X0,s(X1)) = a(X0,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(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),s(n(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(f172,plain,
! [X0,X1,X2] :
( ~ mem(X0,X1)
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f52]) ).
fof(f173,plain,
subq(u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))),a(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))),
inference(forward_demodulation,[status(thm)],[f59,f169]) ).
fof(f182,plain,
! [X0,X1,X2] :
( ~ mem(X0,s(X2))
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f53]) ).
fof(f183,plain,
! [X0,X1] :
( ~ mem(X0,X1)
| mem(X0,n(X1)) ),
inference(paramodulation,[status(thm)],[f60,f172]) ).
fof(f184,plain,
! [X0,X1] : mem(X0,a(X1,X0)),
inference(resolution,[status(thm)],[f182,f170]) ).
fof(f185,plain,
! [X0] : mem(X0,n(X0)),
inference(paramodulation,[status(thm)],[f60,f184]) ).
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(f190,plain,
! [X0,X1,X2] :
( mem(X0,X2)
| ~ mem(X0,a(X2,X1))
| X0 = X1 ),
inference(resolution,[status(thm)],[f188,f47]) ).
fof(f193,plain,
! [X0,X1] :
( mem(X1,X0)
| ~ mem(X1,n(X0))
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f60,f190]) ).
fof(f219,plain,
! [X0,X1] :
( subq(s(X0),X1)
| X0 = sK0_skl(X1,s(X0)) ),
inference(resolution,[status(thm)],[f33,f47]) ).
fof(f220,plain,
! [X0] : subq(e,X0),
inference(resolution,[status(thm)],[f33,f44]) ).
fof(f233,plain,
! [X0] :
( ~ subq(X0,e)
| X0 = e ),
inference(resolution,[status(thm)],[f220,f36]) ).
fof(f353,plain,
! [X0] :
( e = s(X0)
| sK0_skl(e,s(X0)) = X0 ),
inference(resolution,[status(thm)],[f219,f233]) ).
fof(f376,plain,
! [X0] :
( ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))))
| mem(X0,a(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),n(n(n(e))))) ),
inference(resolution,[status(thm)],[f32,f173]) ).
fof(f411,plain,
! [X0] :
( sK0_skl(e,s(X0)) = X0
| mem(X0,e) ),
inference(paramodulation,[status(thm)],[f353,f170]) ).
fof(f516,plain,
! [X0] : sK0_skl(e,s(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f411,f44]) ).
fof(f546,plain,
! [X0] :
( mem(X0,u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))))
| n(n(n(e))) = X0
| ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e)))))) ),
inference(resolution,[status(thm)],[f376,f190]) ).
fof(f552,plain,
! [X0] :
( mem(X0,u(s(n(s(n(e)))),n(s(n(n(e))))))
| n(n(n(e))) = X0
| ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))))
| mem(X0,s(u(n(e),n(s(n(e)))))) ),
inference(resolution,[status(thm)],[f546,f51]) ).
fof(f574,plain,
! [X0] :
( mem(X0,s(u(n(e),n(s(n(e))))))
| mem(X0,n(s(n(n(e)))))
| X0 = n(n(n(e)))
| mem(X0,s(n(s(n(e)))))
| ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e)))))) ),
inference(resolution,[status(thm)],[f552,f51]) ).
fof(f585,plain,
! [X0] :
( mem(X0,s(u(n(e),n(s(n(e))))))
| mem(X0,s(n(s(n(e)))))
| s(n(n(e))) = X0
| mem(X0,s(n(n(e))))
| ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))))
| n(n(n(e))) = X0 ),
inference(resolution,[status(thm)],[f574,f193]) ).
fof(f761,plain,
! [X0] :
( mem(X0,s(n(s(n(e)))))
| mem(X0,s(u(n(e),n(s(n(e))))))
| ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))))
| X0 = s(n(n(e)))
| X0 = n(n(n(e)))
| X0 = n(n(e)) ),
inference(resolution,[status(thm)],[f585,f47]) ).
fof(f777,plain,
! [X0] :
( s(n(n(e))) = X0
| X0 = n(s(n(e)))
| n(n(n(e))) = X0
| mem(X0,s(u(n(e),n(s(n(e))))))
| n(n(e)) = X0
| ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e)))))) ),
inference(resolution,[status(thm)],[f761,f47]) ).
fof(f865,plain,
! [X0] :
( n(n(n(e))) = X0
| X0 = u(n(e),n(s(n(e))))
| s(n(n(e))) = X0
| X0 = n(s(n(e)))
| ~ mem(X0,u(u(s(u(n(e),n(s(n(e))))),u(s(n(s(n(e)))),n(s(n(n(e)))))),a(s(s(n(e))),n(n(n(e))))))
| n(n(e)) = X0 ),
inference(resolution,[status(thm)],[f777,f47]) ).
fof(f913,plain,
! [X0] :
( X0 = u(n(e),n(s(n(e))))
| n(s(n(e))) = X0
| n(n(e)) = X0
| X0 = n(n(n(e)))
| ~ mem(X0,a(s(s(n(e))),n(n(n(e)))))
| X0 = s(n(n(e))) ),
inference(resolution,[status(thm)],[f865,f53]) ).
fof(f959,plain,
! [X0] :
( ~ mem(X0,s(s(n(e))))
| X0 = n(n(e))
| n(s(n(e))) = X0
| X0 = s(n(n(e)))
| X0 = n(n(n(e)))
| u(n(e),n(s(n(e)))) = X0 ),
inference(resolution,[status(thm)],[f913,f172]) ).
fof(f1113,definition,
( sQ89_spl
<=> n(e) = n(n(e)) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1114,plain,
( ~ sQ89_spl
| n(n(e)) = n(e) ),
inference(component_clause,[status(thm)],[f1113]) ).
fof(f1115,plain,
( sQ89_spl
| n(n(e)) != n(e) ),
inference(component_clause,[status(thm)],[f1113]) ).
fof(f1153,plain,
( ~ sQ89_spl
| mem(n(e),n(e)) ),
inference(paramodulation,[status(thm)],[f1114,f185]) ).
fof(f1181,plain,
( ~ sQ89_spl
| mem(n(e),e)
| e = n(e) ),
inference(resolution,[status(thm)],[f1153,f193]) ).
fof(f1182,definition,
( sQ91_spl
<=> e = n(e) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1183,plain,
( ~ sQ91_spl
| n(e) = e ),
inference(component_clause,[status(thm)],[f1182]) ).
fof(f1185,definition,
( sQ92_spl
<=> mem(n(e),e) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1186,plain,
( ~ sQ92_spl
| mem(n(e),e) ),
inference(component_clause,[status(thm)],[f1185]) ).
fof(f1188,plain,
( ~ sQ89_spl
| sQ92_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1181,f1182,f1185,f1113]) ).
fof(f1189,plain,
( ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1186,f44]) ).
fof(f1190,plain,
~ sQ92_spl,
inference(contradiction_clause,[status(thm)],[f1189]) ).
fof(f1196,plain,
( ~ sQ91_spl
| mem(e,e) ),
inference(paramodulation,[status(thm)],[f1183,f185]) ).
fof(f1201,plain,
( ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1196,f44]) ).
fof(f1202,plain,
~ sQ91_spl,
inference(contradiction_clause,[status(thm)],[f1201]) ).
fof(f1232,definition,
( sQ94_spl
<=> mem(n(n(e)),e) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1233,plain,
( ~ sQ94_spl
| mem(n(n(e)),e) ),
inference(component_clause,[status(thm)],[f1232]) ).
fof(f1236,plain,
( ~ sQ94_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1233,f44]) ).
fof(f1237,plain,
~ sQ94_spl,
inference(contradiction_clause,[status(thm)],[f1236]) ).
fof(f1378,definition,
( sQ106_spl
<=> subq(e,sK2_skl(p(e))) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1380,plain,
( sQ106_spl
| ~ subq(e,sK2_skl(p(e))) ),
inference(component_clause,[status(thm)],[f1378]) ).
fof(f1386,plain,
( sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1380,f220]) ).
fof(f1387,plain,
sQ106_spl,
inference(contradiction_clause,[status(thm)],[f1386]) ).
fof(f1713,definition,
! [X0] :
( sQ138_spl
<=> mem(n(n(e)),X0) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1714,plain,
! [X0] :
( ~ sQ138_spl
| mem(n(n(e)),X0) ),
inference(component_clause,[status(thm)],[f1713]) ).
fof(f1724,plain,
! [X0] :
( ~ sQ138_spl
| ~ mem(n(n(e)),X0) ),
inference(resolution,[status(thm)],[f1714,f57]) ).
fof(f1733,plain,
( ~ sQ138_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1724,f1714]) ).
fof(f1734,plain,
~ sQ138_spl,
inference(contradiction_clause,[status(thm)],[f1733]) ).
fof(f1849,plain,
( s(n(e)) = s(n(n(e)))
| u(n(e),n(s(n(e)))) = s(n(e))
| n(s(n(e))) = s(n(e))
| s(n(e)) = n(n(e))
| n(n(n(e))) = s(n(e)) ),
inference(resolution,[status(thm)],[f959,f170]) ).
fof(f1850,definition,
( sQ150_spl
<=> n(n(n(e))) = s(n(e)) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1851,plain,
( ~ sQ150_spl
| n(n(n(e))) = s(n(e)) ),
inference(component_clause,[status(thm)],[f1850]) ).
fof(f1853,definition,
( sQ151_spl
<=> s(n(e)) = n(n(e)) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1854,plain,
( ~ sQ151_spl
| n(n(e)) = s(n(e)) ),
inference(component_clause,[status(thm)],[f1853]) ).
fof(f1856,definition,
( sQ152_spl
<=> n(s(n(e))) = s(n(e)) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1857,plain,
( ~ sQ152_spl
| s(n(e)) = n(s(n(e))) ),
inference(component_clause,[status(thm)],[f1856]) ).
fof(f1859,definition,
( sQ153_spl
<=> u(n(e),n(s(n(e)))) = s(n(e)) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1860,plain,
( ~ sQ153_spl
| s(n(e)) = u(n(e),n(s(n(e)))) ),
inference(component_clause,[status(thm)],[f1859]) ).
fof(f1862,definition,
( sQ154_spl
<=> s(n(e)) = s(n(n(e))) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1863,plain,
( ~ sQ154_spl
| s(n(e)) = s(n(n(e))) ),
inference(component_clause,[status(thm)],[f1862]) ).
fof(f1865,plain,
( sQ154_spl
| sQ153_spl
| sQ152_spl
| sQ151_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f1849,f1850,f1853,f1856,f1859,f1862]) ).
fof(f1899,plain,
! [X0] :
( ~ sQ151_spl
| ~ mem(X0,n(e))
| mem(X0,s(n(e))) ),
inference(paramodulation,[status(thm)],[f1854,f183]) ).
fof(f1989,plain,
( ~ sQ152_spl
| mem(s(n(e)),s(n(e))) ),
inference(paramodulation,[status(thm)],[f1857,f185]) ).
fof(f2020,plain,
( ~ sQ154_spl
| sK0_skl(e,s(n(e))) = n(n(e)) ),
inference(paramodulation,[status(thm)],[f1863,f516]) ).
fof(f2079,plain,
( ~ sQ154_spl
| n(e) = n(n(e)) ),
inference(forward_demodulation,[status(thm)],[f516,f2020]) ).
fof(f2080,plain,
( ~ sQ154_spl
| sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2079,f1115]) ).
fof(f2081,plain,
( ~ sQ154_spl
| sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f2080]) ).
fof(f2134,plain,
( ~ sQ150_spl
| mem(n(n(e)),s(n(e))) ),
inference(paramodulation,[status(thm)],[f1851,f185]) ).
fof(f2223,plain,
! [X0] :
( ~ sQ153_spl
| mem(X0,s(n(e)))
| ~ mem(X0,n(e)) ),
inference(paramodulation,[status(thm)],[f1860,f52]) ).
fof(f2310,plain,
! [X0] :
( ~ sQ153_spl
| ~ mem(X0,n(e))
| n(e) = X0 ),
inference(resolution,[status(thm)],[f2223,f47]) ).
fof(f2332,plain,
( ~ sQ153_spl
| n(e) = e ),
inference(resolution,[status(thm)],[f2310,f185]) ).
fof(f2334,plain,
( ~ sQ153_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f2332,f1182,f1859]) ).
fof(f2422,plain,
( ~ sQ150_spl
| n(n(e)) = n(e) ),
inference(resolution,[status(thm)],[f2134,f47]) ).
fof(f2423,plain,
( ~ sQ150_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f2422,f1113,f1850]) ).
fof(f2673,plain,
! [X0] :
( ~ sQ151_spl
| X0 = n(e)
| ~ mem(X0,n(e)) ),
inference(resolution,[status(thm)],[f1899,f47]) ).
fof(f2698,plain,
( ~ sQ151_spl
| e = n(e) ),
inference(resolution,[status(thm)],[f2673,f185]) ).
fof(f2700,plain,
( ~ sQ151_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f2698,f1182,f1853]) ).
fof(f2712,plain,
( ~ sQ152_spl
| s(n(e)) = n(e) ),
inference(resolution,[status(thm)],[f1989,f47]) ).
fof(f2746,plain,
( ~ sQ152_spl
| mem(n(e),n(e)) ),
inference(paramodulation,[status(thm)],[f2712,f170]) ).
fof(f2920,plain,
( ~ sQ152_spl
| mem(n(e),e)
| e = n(e) ),
inference(resolution,[status(thm)],[f2746,f193]) ).
fof(f2921,plain,
( ~ sQ152_spl
| sQ92_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f2920,f1182,f1185,f1856]) ).
fof(f2922,plain,
$false,
inference(sat_refutation,[status(thm)],[f1188,f1190,f1202,f1237,f1387,f1734,f1865,f2081,f2334,f2423,f2700,f2921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV571+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n011.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 07:27:55 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 113.28/14.84 % Refutation found
% 113.28/14.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 113.28/14.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 66.02/16.06 % Elapsed time: 15.490056 seconds
% 66.02/16.06 % CPU time: 111.118534 seconds
% 66.02/16.06 % Total memory used: 505.062 MB
% 66.02/16.06 % Net memory used: 456.217 MB
%------------------------------------------------------------------------------