%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV561+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 : Fri Sep 25 03:02:39 PM UTC 2026
% Result : Theorem 57.24s 19.00s
% Output : CNFRefutation 57.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 100 ( 24 unt; 0 def)
% Number of atoms : 250 ( 84 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 233 ( 83 ~; 126 |; 16 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn 140 !; 5 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',subq_def) ).
fof(f3,axiom,
! [X0,X1] :
( disj(X0,X1)
<=> ~ ? [X2] :
( mem(X2,X1)
& mem(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',disj_def) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',s_ax) ).
fof(f6,axiom,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
<=> ( mem(X0,X2)
| mem(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',u_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',n_def) ).
fof(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET010+0.ax',p_ax) ).
fof(f26,conjecture,
disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disj_17_4108) ).
fof(f27,negated_conjecture,
~ disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ ? [X2] :
( mem(X2,X1)
& mem(X2,X0) )
=> disj(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f30,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( ~ mem(X2,X0)
| mem(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X2] :
( mem(X2,X1)
& mem(X2,X0) )
| disj(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ subq(X0,X1)
| ! [X2] :
( ~ mem(X2,X0)
| mem(X2,X1) ) )
& ( ? [X2] :
( mem(X2,X0)
& ~ mem(X2,X1) )
| subq(X0,X1) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ subq(X0,X1)
| ! [X3] :
( ~ mem(X3,X0)
| mem(X3,X1) ) )
& ( ? [X2] :
( mem(X2,X0)
& ~ mem(X2,X1) )
| subq(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ subq(X0,X1)
| ! [X3] :
( ~ mem(X3,X0)
| mem(X3,X1) ) )
& ( ( mem(sK0(X0,X1),X0)
& ~ mem(sK0(X0,X1),X1) )
| subq(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ( mem(sK1(X0,X1),X1)
& mem(sK1(X0,X1),X0) )
| disj(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f33]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ mem(X0,s(X1))
| X0 = X1 )
& ( X0 != X1
| mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) )
& ( ( ~ mem(X0,X2)
& ~ mem(X0,X1) )
| mem(X0,u(X1,X2)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) )
& ( ( ~ mem(X0,X2)
& ~ mem(X0,X1) )
| mem(X0,u(X1,X2)) ) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ mem(X0,p(X1))
| subq(X0,X1) )
& ( ~ subq(X0,X1)
| mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f44,plain,
! [X3,X0,X1] :
( ~ subq(X0,X1)
| ~ mem(X3,X0)
| mem(X3,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0,X1] :
( mem(sK1(X0,X1),X1)
| disj(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
! [X0,X1] :
( mem(sK1(X0,X1),X0)
| disj(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f52,plain,
! [X0,X1] :
( X0 != X1
| mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ mem(X0,X2)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ mem(X0,X1)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f59,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f60,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f61,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| subq(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f63,plain,
~ disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
inference(cnf_transformation,[],[f28]) ).
fof(f64,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f60,f59]) ).
fof(f65,plain,
~ disj(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(definition_unfolding,[],[f63,f64,f64,f59,f64,f64,f64]) ).
fof(f66,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f52]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X2,X1)
| ~ mem(X2,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( disj(X0,X1)
| mem(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( disj(X0,X1)
| mem(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_55,plain,
! [X0: $i] : ~ mem(X0,e),
inference(cnf_transformation,[],[f50]) ).
tcf(c_56,plain,
! [X0: $i] : mem(X0,s(X0)),
inference(cnf_transformation,[],[f66]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X2,X1))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,X2)
| mem(X0,X1)
| ~ mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ mem(X0,p(X1)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_66,negated_conjecture,
~ disj(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(cnf_transformation,[],[f65]) ).
tcf(c_67,plain,
mem(e,s(e)),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_68,plain,
~ mem(e,e),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_74,plain,
( ( e = e )
| ~ mem(e,s(e)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( disj(X0,X1)
| mem(sK1(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( mem(sK1(X0,X1),X0)
| disj(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_53]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( disj(X0,X1)
| mem(sK1(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_106]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] :
( mem(sK1(X0,X1),X1)
| ( p(s(s(u(e,s(e))))) != X0 )
| ( u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_66]) ).
tcf(c_229,plain,
mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(unflattening,[status(thm)],[c_228]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( mem(sK1(X0,X1),X0)
| ( p(s(s(u(e,s(e))))) != X0 )
| ( u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_107,c_66]) ).
tcf(c_234,plain,
mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),p(s(s(u(e,s(e)))))),
inference(unflattening,[status(thm)],[c_233]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( mem(X0,X2)
| ~ mem(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_785,plain,
! [X0: $i,X1: $i] :
( mem(X0,u(X1,s(X0)))
| ~ mem(X0,s(X0)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_786,plain,
( mem(e,u(e,s(e)))
| ~ mem(e,s(e)) ),
inference(instantiation,[status(thm)],[c_785]) ).
tcf(c_1202,plain,
subq(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),s(s(u(e,s(e))))),
inference(superposition,[status(thm)],[c_234,c_65]) ).
tcf(c_1204,plain,
! [X0: $i,X1: $i] :
( mem(X0,X1)
| ~ subq(s(X0),X1) ),
inference(superposition,[status(thm)],[c_56,c_51]) ).
tcf(c_1205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( mem(X3,X2)
| ~ mem(X3,X0)
| ~ subq(u(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_58,c_51]) ).
tcf(c_1206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( mem(X3,X2)
| ~ mem(X3,X1)
| ~ subq(u(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_59,c_51]) ).
tcf(c_1213,plain,
( mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))) ),
inference(superposition,[status(thm)],[c_229,c_60]) ).
tcf(c_1229,plain,
( mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) ) ),
inference(superposition,[status(thm)],[c_1213,c_57]) ).
tcf(c_1240,plain,
( mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),s(s(u(e,s(e)))))
| mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),s(u(u(e,s(e)),s(u(e,s(e))))))
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) ) ),
inference(superposition,[status(thm)],[c_1229,c_60]) ).
tcf(c_1345,plain,
( mem(sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),s(s(u(e,s(e)))))
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(u(e,s(e)),s(u(e,s(e)))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) ) ),
inference(superposition,[status(thm)],[c_1240,c_57]) ).
tcf(c_1376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( mem(X0,X2)
| ~ mem(X1,u(X3,s(X1)))
| ( X2 != u(X3,s(X1)) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_377]) ).
tcf(c_1377,plain,
( mem(e,e)
| ~ mem(e,u(e,s(e)))
| ( e != e )
| ( e != u(e,s(e)) ) ),
inference(instantiation,[status(thm)],[c_1376]) ).
tcf(c_1593,plain,
( ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(u(e,s(e)),s(u(e,s(e)))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) ) ),
inference(superposition,[status(thm)],[c_1345,c_57]) ).
tcf(c_2315,plain,
( subq(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(s(u(e,s(e)))))
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(u(e,s(e)),s(u(e,s(e)))) ) ),
inference(superposition,[status(thm)],[c_1593,c_1202]) ).
tcf(c_2426,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = u(X1,s(X2)) )
| ~ mem(X0,s(u(X1,s(X2)))) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_2427,plain,
( ( e = u(e,s(e)) )
| ~ mem(e,s(u(e,s(e)))) ),
inference(instantiation,[status(thm)],[c_2426]) ).
tcf(c_2432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = u(X0,s(X1)) )
| ( X3 != X2 )
| ( u(X0,s(X1)) != X2 ) ),
inference(instantiation,[status(thm)],[c_376]) ).
tcf(c_2433,plain,
( ( e = u(e,s(e)) )
| ( e != e )
| ( u(e,s(e)) != e ) ),
inference(instantiation,[status(thm)],[c_2432]) ).
tcf(c_2514,plain,
! [X0: $i] :
( mem(X0,s(s(u(e,s(e)))))
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(u(e,s(e)),s(u(e,s(e)))) )
| ~ mem(X0,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(superposition,[status(thm)],[c_2315,c_1206]) ).
tcf(c_2569,plain,
( mem(u(u(e,s(e)),s(u(e,s(e)))),s(s(u(e,s(e)))))
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(u(e,s(e)),s(u(e,s(e)))) ) ),
inference(superposition,[status(thm)],[c_56,c_2514]) ).
tcf(c_2946,plain,
( ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = u(u(e,s(e)),s(u(e,s(e)))) ) ),
inference(superposition,[status(thm)],[c_2569,c_57]) ).
tcf(c_3086,plain,
( subq(u(u(e,s(e)),s(u(e,s(e)))),s(s(u(e,s(e)))))
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) ) ),
inference(superposition,[status(thm)],[c_2946,c_1202]) ).
tcf(c_3356,plain,
! [X0: $i] :
( mem(X0,s(s(u(e,s(e)))))
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_3086,c_1205]) ).
tcf(c_3360,plain,
! [X0: $i] :
( ( s(u(e,s(e))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_3356,c_57]) ).
tcf(c_3364,plain,
! [X0: $i] :
( ( s(u(e,s(e))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) )
| ~ mem(X0,s(e)) ),
inference(superposition,[status(thm)],[c_59,c_3360]) ).
tcf(c_3504,plain,
( ( s(u(e,s(e))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) )
| ( sK1(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) = s(u(e,s(e))) ) ),
inference(superposition,[status(thm)],[c_56,c_3364]) ).
tcf(c_3784,plain,
( subq(s(u(e,s(e))),s(s(u(e,s(e)))))
| ( s(u(e,s(e))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) ) ),
inference(superposition,[status(thm)],[c_3504,c_1202]) ).
tcf(c_3786,plain,
( mem(s(u(e,s(e))),p(s(s(u(e,s(e))))))
| ( s(u(e,s(e))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) ) ),
inference(superposition,[status(thm)],[c_3504,c_234]) ).
tcf(c_4106,plain,
( mem(u(e,s(e)),s(s(u(e,s(e)))))
| ( s(u(e,s(e))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) ) ),
inference(superposition,[status(thm)],[c_3784,c_1204]) ).
tcf(c_4116,plain,
( ( s(u(e,s(e))) = e )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = s(u(e,s(e))) ) ),
inference(superposition,[status(thm)],[c_4106,c_57]) ).
tcf(c_4153,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| ( s(u(e,s(e))) = e )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_4116,c_58]) ).
tcf(c_4360,plain,
( mem(e,s(u(e,s(e))))
| ( s(u(e,s(e))) = e )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ~ mem(e,u(e,s(e))) ),
inference(instantiation,[status(thm)],[c_4153]) ).
tcf(c_5009,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(u(e,s(e))) = e ) ),
inference(global_subsumption_just,[status(thm)],[c_4153,c_67,c_68,c_74,c_786,c_1377,c_2427,c_4360]) ).
tcf(c_5010,plain,
( ( s(u(e,s(e))) = e )
| ( s(u(e,s(e))) = u(e,s(e)) ) ),
inference(renaming,[status(thm)],[c_5009]) ).
tcf(c_5013,plain,
! [X0: $i] :
( ( u(e,s(e)) = X0 )
| ( s(u(e,s(e))) = e )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_5010,c_57]) ).
tcf(c_5245,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ~ mem(e,u(e,s(e))) ),
inference(instantiation,[status(thm)],[c_5013]) ).
tcf(c_5916,plain,
s(u(e,s(e))) = e,
inference(global_subsumption_just,[status(thm)],[c_3786,c_67,c_68,c_74,c_786,c_1377,c_2433,c_5245]) ).
tcf(c_5934,plain,
mem(u(e,s(e)),e),
inference(superposition,[status(thm)],[c_5916,c_56]) ).
tcf(c_6894,plain,
$false,
inference(superposition,[status(thm)],[c_5934,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV561+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n017.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 14:55:31 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 57.24/19.00 % SZS status Started for theBenchmark.p
% 57.24/19.00 % SZS status Theorem for theBenchmark.p
% 57.24/19.00
% 57.24/19.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 57.24/19.00
% 57.24/19.00 % ------ iProver source info
% 57.24/19.00
% 57.24/19.00 % git: date: 2026-07-19 20:42:38 +0200
% 57.24/19.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 57.24/19.00 % git: non_committed_changes: false
% 57.24/19.00
% 57.24/19.00 % ------ Parsing...
% 57.24/19.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 57.24/19.00
% 57.24/19.00 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 57.24/19.00
% 57.24/19.00 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 57.24/19.00
% 57.24/19.00 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 57.24/19.00 % ------ Proving...
% 57.24/19.00 % ------ Problem Properties
% 57.24/19.00
% 57.24/19.00 %
% 57.24/19.00 % clauses 17
% 57.24/19.00 % conjectures 0
% 57.24/19.00 % EPR 3
% 57.24/19.00 % Horn 14
% 57.24/19.00 % unary 4
% 57.24/19.00 % binary 9
% 57.24/19.00 % lits 34
% 57.24/19.00 % lits eq 2
% 57.24/19.00 % fd_pure 0
% 57.24/19.00 % fd_pseudo 0
% 57.24/19.00 % fd_cond 0
% 57.24/19.00 % fd_pseudo_cond 2
% 57.24/19.00 % AC symbols 0
% 57.24/19.00
% 57.24/19.00 % ------ Input Options Time Limit: Unbounded
% 57.24/19.00
% 57.24/19.00
% 57.24/19.00 % ------
% 57.24/19.00 % Current options:
% 57.24/19.00 % ------
% 57.24/19.00
% 57.24/19.00
% 57.24/19.00 %
% 57.24/19.00
% 57.24/19.00 % ------ Proving...
% 57.24/19.00 %
% 57.24/19.00
% 57.24/19.00 % ------ Proving...
% 57.24/19.00 %
% 57.24/19.00
% 57.24/19.00 % ------ Proving...
% 57.24/19.00 %
% 57.24/19.00
% 57.24/19.00 % SZS status Theorem for theBenchmark.p
% 57.24/19.00
% 57.24/19.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 57.24/19.00
% 57.24/19.00
%------------------------------------------------------------------------------