%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV570+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 : n012.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 0.13s 0.76s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 87 ( 15 unt; 6 def)
% Number of atoms : 213 ( 57 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 220 ( 94 ~; 103 |; 12 &)
% ( 10 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 106 ( 104 !; 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(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(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),s(a(s(n(e)),n(n(e))))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ ~ subq(u(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),s(a(s(n(e)),n(n(e))))),a(s(u(n(e),n(s(n(e))))),a(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(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(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),s(a(s(n(e)),n(n(e))))),a(s(u(n(e),n(s(n(e))))),a(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(f180,plain,
subq(a(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e)))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e))))),
inference(backward_demodulation,[status(thm)],[f59,f169]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ~ mem(X0,X1)
| mem(X0,a(X1,X2)) ),
inference(paramodulation,[status(thm)],[f59,f52]) ).
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,f181]) ).
fof(f184,plain,
! [X0,X1,X2] :
( X0 = X2
| mem(X0,X1)
| ~ mem(X0,u(X1,s(X2))) ),
inference(resolution,[status(thm)],[f51,f47]) ).
fof(f186,plain,
! [X0,X1,X2] :
( X0 = X2
| mem(X0,X1)
| ~ mem(X0,a(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f59,f184]) ).
fof(f195,plain,
! [X0] :
( mem(X0,a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e)))))
| ~ mem(X0,a(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e))))) ),
inference(resolution,[status(thm)],[f32,f180]) ).
fof(f220,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| mem(X0,n(X1)) ),
inference(paramodulation,[status(thm)],[f60,f182]) ).
fof(f223,plain,
! [X0,X1,X2] :
( X0 = X1
| X0 = X2
| ~ mem(X0,a(s(X1),X2)) ),
inference(resolution,[status(thm)],[f186,f47]) ).
fof(f224,plain,
! [X0,X1] :
( X0 = X1
| ~ mem(X0,a(e,X1)) ),
inference(resolution,[status(thm)],[f186,f44]) ).
fof(f259,plain,
! [X0] :
( X0 = e
| ~ mem(X0,n(e)) ),
inference(paramodulation,[status(thm)],[f60,f224]) ).
fof(f329,plain,
! [X0] :
( ~ mem(X0,a(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e)))))
| X0 = u(n(e),n(s(n(e))))
| X0 = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[f223,f195]) ).
fof(f335,plain,
! [X0,X1] :
( X0 = X1
| X0 = s(X1)
| ~ mem(X0,n(s(X1))) ),
inference(paramodulation,[status(thm)],[f60,f223]) ).
fof(f545,plain,
! [X0] :
( ~ mem(X0,a(s(n(s(n(e)))),u(n(e),n(s(n(e))))))
| X0 = u(n(e),n(s(n(e))))
| X0 = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[f329,f181]) ).
fof(f552,plain,
! [X0] :
( ~ mem(X0,s(n(s(n(e)))))
| X0 = u(n(e),n(s(n(e))))
| X0 = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[f545,f181]) ).
fof(f558,plain,
( n(s(n(e))) = u(n(e),n(s(n(e))))
| n(s(n(e))) = a(s(n(e)),n(n(e))) ),
inference(resolution,[status(thm)],[f552,f170]) ).
fof(f563,definition,
( sQ28_spl
<=> n(s(n(e))) = a(s(n(e)),n(n(e))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( ~ sQ28_spl
| n(s(n(e))) = a(s(n(e)),n(n(e))) ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f566,definition,
( sQ29_spl
<=> n(s(n(e))) = u(n(e),n(s(n(e)))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ29_spl
| n(s(n(e))) = u(n(e),n(s(n(e)))) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,plain,
( sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f558,f563,f566]) ).
fof(f638,plain,
! [X0] :
( ~ sQ28_spl
| ~ mem(X0,s(n(n(e))))
| mem(X0,n(s(n(e)))) ),
inference(paramodulation,[status(thm)],[f564,f182]) ).
fof(f646,plain,
! [X0] :
( ~ sQ28_spl
| X0 = n(e)
| X0 = s(n(e))
| ~ mem(X0,s(n(n(e)))) ),
inference(resolution,[status(thm)],[f638,f335]) ).
fof(f742,plain,
( ~ sQ28_spl
| n(n(e)) = n(e)
| n(n(e)) = s(n(e)) ),
inference(resolution,[status(thm)],[f646,f170]) ).
fof(f748,definition,
( sQ33_spl
<=> n(n(e)) = s(n(e)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f749,plain,
( ~ sQ33_spl
| n(n(e)) = s(n(e)) ),
inference(component_clause,[status(thm)],[f748]) ).
fof(f751,definition,
( sQ34_spl
<=> n(n(e)) = n(e) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f752,plain,
( ~ sQ34_spl
| n(n(e)) = n(e) ),
inference(component_clause,[status(thm)],[f751]) ).
fof(f754,plain,
( ~ sQ28_spl
| sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f742,f748,f751,f563]) ).
fof(f761,plain,
! [X0] :
( ~ sQ33_spl
| ~ mem(X0,n(e))
| mem(X0,s(n(e))) ),
inference(paramodulation,[status(thm)],[f749,f183]) ).
fof(f764,plain,
! [X0] :
( ~ sQ33_spl
| X0 = n(e)
| ~ mem(X0,n(e)) ),
inference(resolution,[status(thm)],[f761,f47]) ).
fof(f767,plain,
! [X0] :
( ~ sQ33_spl
| ~ mem(X0,s(e))
| X0 = n(e) ),
inference(resolution,[status(thm)],[f764,f220]) ).
fof(f775,plain,
( ~ sQ33_spl
| e = n(e) ),
inference(resolution,[status(thm)],[f767,f170]) ).
fof(f785,plain,
( ~ sQ33_spl
| n(n(e)) = s(e) ),
inference(backward_demodulation,[status(thm)],[f775,f749]) ).
fof(f797,plain,
( ~ sQ33_spl
| n(e) = s(e) ),
inference(forward_demodulation,[status(thm)],[f775,f785]) ).
fof(f798,plain,
( ~ sQ33_spl
| e = s(e) ),
inference(forward_demodulation,[status(thm)],[f775,f797]) ).
fof(f839,plain,
( ~ sQ33_spl
| mem(e,e) ),
inference(paramodulation,[status(thm)],[f798,f170]) ).
fof(f863,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f839,f44]) ).
fof(f864,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f863]) ).
fof(f894,plain,
! [X0] :
( ~ sQ29_spl
| ~ mem(X0,n(e))
| mem(X0,n(s(n(e)))) ),
inference(paramodulation,[status(thm)],[f567,f52]) ).
fof(f897,plain,
! [X0] :
( ~ sQ29_spl
| X0 = n(e)
| X0 = s(n(e))
| ~ mem(X0,n(e)) ),
inference(resolution,[status(thm)],[f894,f335]) ).
fof(f900,plain,
! [X0] :
( ~ sQ29_spl
| ~ mem(X0,s(e))
| X0 = n(e)
| X0 = s(n(e)) ),
inference(resolution,[status(thm)],[f897,f220]) ).
fof(f1069,plain,
( ~ sQ29_spl
| e = n(e)
| e = s(n(e)) ),
inference(resolution,[status(thm)],[f900,f170]) ).
fof(f1075,definition,
( sQ40_spl
<=> e = s(n(e)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1076,plain,
( ~ sQ40_spl
| e = s(n(e)) ),
inference(component_clause,[status(thm)],[f1075]) ).
fof(f1078,definition,
( sQ41_spl
<=> e = n(e) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1079,plain,
( ~ sQ41_spl
| e = n(e) ),
inference(component_clause,[status(thm)],[f1078]) ).
fof(f1081,plain,
( ~ sQ29_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1069,f1075,f1078,f566]) ).
fof(f1113,plain,
( ~ sQ40_spl
| mem(n(e),e) ),
inference(paramodulation,[status(thm)],[f1076,f170]) ).
fof(f1155,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1113,f44]) ).
fof(f1156,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f1155]) ).
fof(f1160,plain,
! [X0] :
( ~ sQ41_spl
| ~ mem(X0,s(e))
| mem(X0,e) ),
inference(paramodulation,[status(thm)],[f1079,f220]) ).
fof(f1163,plain,
! [X0] :
( ~ sQ41_spl
| ~ mem(X0,s(e)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1160,f44]) ).
fof(f1188,plain,
( ~ sQ41_spl
| $false ),
inference(resolution,[status(thm)],[f1163,f170]) ).
fof(f1194,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f1188]) ).
fof(f1195,plain,
! [X0] :
( ~ sQ34_spl
| ~ mem(X0,s(n(e)))
| mem(X0,n(e)) ),
inference(paramodulation,[status(thm)],[f752,f220]) ).
fof(f1267,plain,
! [X0] :
( ~ sQ34_spl
| X0 = e
| ~ mem(X0,s(n(e))) ),
inference(resolution,[status(thm)],[f1195,f259]) ).
fof(f1274,plain,
( ~ sQ34_spl
| n(e) = e ),
inference(resolution,[status(thm)],[f1267,f170]) ).
fof(f1280,plain,
( ~ sQ34_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1274,f1078,f751]) ).
fof(f1282,plain,
$false,
inference(sat_refutation,[status(thm)],[f569,f754,f864,f1081,f1156,f1194,f1280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV570+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.58 % Computer : n012.cluster.edu
% 0.08/0.58 % Model : x86_64 x86_64
% 0.08/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.58 % Memory : 8046.5625MB
% 0.08/0.58 % OS : Linux 6.8.0-71-generic
% 0.08/0.58 % CPULimit : 300
% 0.08/0.58 % WCLimit : 300
% 0.08/0.58 % DateTime : Mon Sep 21 07:27:23 UTC 2026
% 0.08/0.58 % CPUTime :
% 0.08/0.59 % Drodi V4.1.1
% 0.13/0.76 % Refutation found
% 0.13/0.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.78 % Elapsed time: 0.185212 seconds
% 0.13/0.78 % CPU time: 1.129329 seconds
% 0.13/0.78 % Total memory used: 131.012 MB
% 0.13/0.78 % Net memory used: 129.160 MB
%------------------------------------------------------------------------------