%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV567+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 121.46s 24.02s
% Output : CNFRefutation 121.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 8
% Syntax : Number of formulae : 122 ( 22 unt; 0 def)
% Number of atoms : 484 ( 248 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 458 ( 96 ~; 346 |; 11 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 131 !; 2 ?; 73 :)
% 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(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(f26,conjecture,
~ subq(u(a(a(n(s(s(n(e)))),s(n(n(e)))),a(n(e),n(n(e)))),u(s(u(n(e),n(s(n(e))))),n(a(s(n(e)),n(n(e)))))),u(a(u(n(s(s(n(e)))),n(s(n(n(e))))),a(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',nsubq_1950_1948) ).
fof(f27,negated_conjecture,
~ ~ subq(u(a(a(n(s(s(n(e)))),s(n(n(e)))),a(n(e),n(n(e)))),u(s(u(n(e),n(s(n(e))))),n(a(s(n(e)),n(n(e)))))),u(a(u(n(s(s(n(e)))),n(s(n(n(e))))),a(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,
subq(u(a(a(n(s(s(n(e)))),s(n(n(e)))),a(n(e),n(n(e)))),u(s(u(n(e),n(s(n(e))))),n(a(s(n(e)),n(n(e)))))),u(a(u(n(s(s(n(e)))),n(s(n(n(e))))),a(n(e),n(n(e)))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e)))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( ~ mem(X2,X0)
| mem(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f32,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,[],[f29]) ).
fof(f33,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,[],[f32]) ).
fof(f34,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))],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ mem(X0,s(X1))
| X0 = X1 )
& ( X0 != X1
| mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f41,plain,
! [X3,X0,X1] :
( ~ subq(X0,X1)
| ~ mem(X3,X0)
| mem(X3,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f42,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f43,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f45,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f47,plain,
! [X0,X1] :
( X0 != X1
| mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ mem(X0,X2)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ mem(X0,X1)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f58,plain,
subq(u(a(a(n(s(s(n(e)))),s(n(n(e)))),a(n(e),n(n(e)))),u(s(u(n(e),n(s(n(e))))),n(a(s(n(e)),n(n(e)))))),u(a(u(n(s(s(n(e)))),n(s(n(n(e))))),a(n(e),n(n(e)))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e)))))),
inference(cnf_transformation,[],[f28]) ).
fof(f59,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f55,f54]) ).
fof(f60,plain,
subq(u(u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),u(u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),
inference(definition_unfolding,[],[f58,f54,f54,f59,f59,f59,f59,f54,f59,f59,f59,f59,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f59]) ).
fof(f61,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f47]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ mem(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| mem(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X2,X1)
| ~ mem(X2,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_53,plain,
! [X0: $i] : ~ mem(X0,e),
inference(cnf_transformation,[],[f45]) ).
tcf(c_54,plain,
! [X0: $i] : mem(X0,s(X0)),
inference(cnf_transformation,[],[f61]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X2,X1))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,X2)
| mem(X0,X1)
| ~ mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_64,negated_conjecture,
subq(u(u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),u(u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),
inference(cnf_transformation,[],[f60]) ).
tcf(c_65,plain,
mem(e,s(e)),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_66,plain,
~ mem(e,e),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_69,plain,
( subq(e,e)
| mem(sK0(e,e),e) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_71,plain,
( ( e = e )
| ~ mem(e,s(e)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_72,plain,
( subq(e,e)
| ~ mem(sK0(e,e),e) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subq(X0,X2)
| ~ subq(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_567,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_57,c_51]) ).
tcf(c_574,plain,
! [X0: $i] :
( mem(X0,u(u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))))
| ~ mem(X0,u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))) ),
inference(superposition,[status(thm)],[c_64,c_567]) ).
tcf(c_586,plain,
! [X0: $i,X1: $i] :
( mem(X0,u(X1,s(X0)))
| ~ mem(X0,s(X0)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_587,plain,
( mem(e,u(e,s(e)))
| ~ mem(e,s(e)) ),
inference(instantiation,[status(thm)],[c_586]) ).
tcf(c_608,plain,
! [X0: $i] :
( mem(X0,u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(X0,u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))) ),
inference(superposition,[status(thm)],[c_574,c_58]) ).
tcf(c_611,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X1,X2)
| ~ mem(X1,u(X0,s(X1)))
| ~ subq(u(X0,s(X1)),X2) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_612,plain,
( mem(e,e)
| ~ mem(e,u(e,s(e)))
| ~ subq(u(e,s(e)),e) ),
inference(instantiation,[status(thm)],[c_611]) ).
tcf(c_619,plain,
! [X0: $i] :
( mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(X0,u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))) ),
inference(superposition,[status(thm)],[c_608,c_58]) ).
tcf(c_623,plain,
! [X0: $i] :
( mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(X0,u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(superposition,[status(thm)],[c_57,c_619]) ).
tcf(c_658,plain,
! [X0: $i] :
( mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(X0,u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(superposition,[status(thm)],[c_623,c_58]) ).
tcf(c_662,plain,
! [X0: $i] :
( mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,u(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(superposition,[status(thm)],[c_658,c_58]) ).
tcf(c_665,plain,
! [X0: $i] :
( mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_56,c_662]) ).
tcf(c_677,plain,
! [X0: $i] :
( mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_665,c_58]) ).
tcf(c_681,plain,
! [X0: $i] :
( mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_677,c_55]) ).
tcf(c_685,plain,
! [X0: $i] :
( mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_681,c_55]) ).
tcf(c_698,plain,
! [X0: $i] :
( mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_56,c_685]) ).
tcf(c_702,plain,
! [X0: $i] :
( mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))))
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_698,c_55]) ).
tcf(c_729,plain,
! [X0: $i] :
( mem(X0,s(s(u(e,s(e)))))
| mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_702,c_58]) ).
tcf(c_733,plain,
! [X0: $i] :
( mem(X0,s(s(u(e,s(e)))))
| mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_729,c_55]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( subq(u(X0,s(X1)),X3)
| ~ subq(X2,X4)
| ( X3 != X4 )
| ( u(X0,s(X1)) != X2 ) ),
inference(instantiation,[status(thm)],[c_208]) ).
tcf(c_739,plain,
( subq(u(e,s(e)),e)
| ~ subq(e,e)
| ( e != e )
| ( u(e,s(e)) != e ) ),
inference(instantiation,[status(thm)],[c_738]) ).
tcf(c_741,plain,
! [X0: $i] :
( mem(X0,s(s(u(e,s(e)))))
| mem(X0,s(s(s(u(e,s(e))))))
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_733,c_55]) ).
tcf(c_750,plain,
! [X0: $i] :
( mem(X0,s(s(u(e,s(e)))))
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_741,c_55]) ).
tcf(c_754,plain,
! [X0: $i] :
( ( s(u(e,s(e))) = X0 )
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_750,c_55]) ).
tcf(c_790,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_54,c_754]) ).
tcf(c_793,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_790,c_58]) ).
tcf(c_794,plain,
! [X0: $i] :
( mem(X0,u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_790,c_56]) ).
tcf(c_906,plain,
( mem(u(e,s(e)),u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_54,c_794]) ).
tcf(c_919,plain,
( mem(u(e,s(e)),e)
| mem(u(e,s(e)),s(e))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_906,c_58]) ).
tcf(c_930,plain,
( mem(u(e,s(e)),e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_919,c_55]) ).
tcf(c_932,plain,
( mem(u(e,s(e)),e)
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(e,s(e))) = u(e,s(e)) ) ),
inference(global_subsumption_just,[status(thm)],[c_930,c_65,c_66,c_69,c_71,c_72,c_587,c_612,c_739,c_930]) ).
tcf(c_933,plain,
( mem(u(e,s(e)),e)
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(renaming,[status(thm)],[c_932]) ).
tcf(c_1086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( u(X0,s(X1)) = X2 )
| ~ mem(u(X0,s(X1)),s(X2)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1087,plain,
( ( u(e,s(e)) = e )
| ~ mem(u(e,s(e)),s(e)) ),
inference(instantiation,[status(thm)],[c_1086]) ).
tcf(c_1198,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_793,c_55]) ).
tcf(c_1252,plain,
! [X0: $i] :
( ( u(e,s(e)) = X0 )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_1198,c_55]) ).
tcf(c_1271,plain,
! [X0: $i] :
( ( u(e,s(e)) = X0 )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) )
| ~ mem(X0,e) ),
inference(superposition,[status(thm)],[c_56,c_1252]) ).
tcf(c_1286,plain,
! [X0: $i] : ~ mem(X0,e),
inference(global_subsumption_just,[status(thm)],[c_1271,c_53]) ).
tcf(c_1289,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_933,c_1286]) ).
tcf(c_1296,plain,
! [X0: $i] :
( mem(X0,u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ~ mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e)))))) ),
inference(superposition,[status(thm)],[c_1289,c_57]) ).
tcf(c_1397,plain,
! [X0: $i] :
( mem(X0,u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_56,c_1296]) ).
tcf(c_1437,plain,
( mem(u(e,s(e)),u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_54,c_1397]) ).
tcf(c_1500,plain,
( mem(u(e,s(e)),e)
| mem(u(e,s(e)),s(e))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_1437,c_58]) ).
tcf(c_1511,plain,
( mem(u(e,s(e)),e)
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(e,s(e))) = u(e,s(e)) ) ),
inference(global_subsumption_just,[status(thm)],[c_1500,c_65,c_66,c_69,c_71,c_72,c_587,c_612,c_739,c_1087,c_1500]) ).
tcf(c_1512,plain,
( mem(u(e,s(e)),e)
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(renaming,[status(thm)],[c_1511]) ).
tcf(c_1514,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_1512,c_1286]) ).
tcf(c_1519,plain,
! [X0: $i] :
( mem(X0,u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) )
| ~ mem(X0,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(superposition,[status(thm)],[c_1514,c_57]) ).
tcf(c_1618,plain,
( mem(u(u(e,s(e)),s(u(e,s(e)))),u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_54,c_1519]) ).
tcf(c_1625,plain,
( mem(u(u(e,s(e)),s(u(e,s(e)))),e)
| mem(u(u(e,s(e)),s(u(e,s(e)))),s(e))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_1618,c_58]) ).
tcf(c_1765,plain,
( mem(u(u(e,s(e)),s(u(e,s(e)))),e)
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_1625,c_55]) ).
tcf(c_1776,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(u(e,s(e)),s(u(e,s(e))))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_1765,c_1286]) ).
tcf(c_1777,plain,
! [X0: $i] :
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_1776,c_55]) ).
tcf(c_1866,plain,
( subq(u(u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),s(u(e,s(e)))),s(u(u(e,s(e)),u(e,s(e))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(s(u(e,s(e))),u(e,s(e))),s(u(s(u(e,s(e))),u(e,s(e))))))),u(u(u(u(s(s(u(e,s(e)))),s(s(s(u(e,s(e)))))),u(u(e,s(e)),s(u(e,s(e))))),s(u(u(e,s(e)),u(e,s(e))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),u(e,s(e)))))))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_1776,c_64]) ).
tcf(c_1867,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ~ mem(e,u(e,s(e))) ),
inference(instantiation,[status(thm)],[c_1777]) ).
tcf(c_2064,plain,
( ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(e,s(e))) = u(e,s(e)) ) ),
inference(global_subsumption_just,[status(thm)],[c_1866,c_65,c_587,c_1867]) ).
tcf(c_2065,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = u(e,s(e)) ) ),
inference(renaming,[status(thm)],[c_2064]) ).
tcf(c_2068,plain,
! [X0: $i] :
( mem(X0,u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_2065,c_57]) ).
tcf(c_2407,plain,
( mem(u(e,s(e)),u(e,s(e)))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e ) ),
inference(superposition,[status(thm)],[c_54,c_2068]) ).
tcf(c_2466,plain,
( mem(u(e,s(e)),e)
| mem(u(e,s(e)),s(e))
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e ) ),
inference(superposition,[status(thm)],[c_2407,c_58]) ).
tcf(c_2468,plain,
( mem(u(e,s(e)),e)
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(e,s(e))) = u(e,s(e)) ) ),
inference(global_subsumption_just,[status(thm)],[c_2466,c_65,c_66,c_69,c_71,c_72,c_587,c_612,c_739,c_1087,c_2466]) ).
tcf(c_2469,plain,
( mem(u(e,s(e)),e)
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e ) ),
inference(renaming,[status(thm)],[c_2468]) ).
tcf(c_2471,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e ) ),
inference(superposition,[status(thm)],[c_2469,c_1286]) ).
tcf(c_2474,plain,
! [X0: $i] :
( mem(X0,e)
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_2471,c_56]) ).
tcf(c_2570,plain,
( mem(e,e)
| ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ~ mem(e,u(e,s(e))) ),
inference(instantiation,[status(thm)],[c_2474]) ).
tcf(c_2850,plain,
( ( s(s(u(e,s(e)))) = u(e,s(e)) )
| ( s(u(e,s(e))) = u(e,s(e)) ) ),
inference(global_subsumption_just,[status(thm)],[c_2474,c_65,c_66,c_587,c_2570]) ).
tcf(c_2851,plain,
( ( s(u(e,s(e))) = u(e,s(e)) )
| ( s(s(u(e,s(e)))) = u(e,s(e)) ) ),
inference(renaming,[status(thm)],[c_2850]) ).
tcf(c_2852,plain,
! [X0: $i] :
( ( s(u(e,s(e))) = X0 )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_2851,c_55]) ).
tcf(c_3225,plain,
! [X0: $i] :
( ( s(u(e,s(e))) = X0 )
| ( s(u(e,s(e))) = u(e,s(e)) )
| ~ mem(X0,s(e)) ),
inference(superposition,[status(thm)],[c_57,c_2852]) ).
tcf(c_3233,plain,
( ( s(u(e,s(e))) = e )
| ( s(u(e,s(e))) = u(e,s(e)) ) ),
inference(superposition,[status(thm)],[c_54,c_3225]) ).
tcf(c_3239,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_3233,c_55]) ).
tcf(c_3244,plain,
( mem(u(e,s(e)),u(e,s(e)))
| ( s(u(e,s(e))) = e ) ),
inference(superposition,[status(thm)],[c_3233,c_54]) ).
tcf(c_3359,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ~ mem(e,u(e,s(e))) ),
inference(instantiation,[status(thm)],[c_3239]) ).
tcf(c_3587,plain,
s(u(e,s(e))) = e,
inference(global_subsumption_just,[status(thm)],[c_3244,c_65,c_66,c_69,c_71,c_72,c_587,c_612,c_739,c_3359]) ).
tcf(c_3595,plain,
mem(u(e,s(e)),e),
inference(superposition,[status(thm)],[c_3587,c_54]) ).
tcf(c_3891,plain,
$false,
inference(superposition,[status(thm)],[c_3595,c_1286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV567+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n017.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 14:56:06 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 121.46/24.02 % SZS status Started for theBenchmark.p
% 121.46/24.02 % SZS status Theorem for theBenchmark.p
% 121.46/24.02
% 121.46/24.02 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 121.46/24.02
% 121.46/24.02 % ------ iProver source info
% 121.46/24.02
% 121.46/24.02 % git: date: 2026-07-19 20:42:38 +0200
% 121.46/24.02 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 121.46/24.02 % git: non_committed_changes: false
% 121.46/24.02
% 121.46/24.02 % ------ Parsing...
% 121.46/24.02 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 121.46/24.02
% 121.46/24.02 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 121.46/24.02
% 121.46/24.02 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 121.46/24.02
% 121.46/24.02 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 121.46/24.02 % ------ Proving...
% 121.46/24.02 % ------ Problem Properties
% 121.46/24.02
% 121.46/24.02 %
% 121.46/24.02 % clauses 16
% 121.46/24.02 % conjectures 1
% 121.46/24.02 % EPR 3
% 121.46/24.02 % Horn 13
% 121.46/24.02 % unary 3
% 121.46/24.02 % binary 9
% 121.46/24.02 % lits 33
% 121.46/24.02 % lits eq 2
% 121.46/24.02 % fd_pure 0
% 121.46/24.02 % fd_pseudo 0
% 121.46/24.02 % fd_cond 0
% 121.46/24.02 % fd_pseudo_cond 2
% 121.46/24.02 % AC symbols 0
% 121.46/24.02
% 121.46/24.02 % ------ Input Options Time Limit: Unbounded
% 121.46/24.02
% 121.46/24.02
% 121.46/24.02 % ------
% 121.46/24.02 % Current options:
% 121.46/24.02 % ------
% 121.46/24.02
% 121.46/24.02
% 121.46/24.02 %
% 121.46/24.02
% 121.46/24.02 % ------ Proving...
% 121.46/24.02 %
% 121.46/24.02
% 121.46/24.02 % SZS status Theorem for theBenchmark.p
% 121.46/24.02
% 121.46/24.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 121.46/24.02
% 121.46/24.02
%------------------------------------------------------------------------------