%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV572+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 03:02:47 PM UTC 2026
% Result : Theorem 10.71s 7.76s
% Output : CNFRefutation 10.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 7
% Syntax : Number of formulae : 111 ( 20 unt; 0 def)
% Number of atoms : 479 ( 221 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 468 ( 100 ~; 352 |; 11 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 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 : 135 ( 0 sgn 133 !; 2 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',subq_def) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET010+0.ax',u_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',n_def) ).
fof(f26,conjecture,
~ subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nsubq_4703_4702) ).
fof(f27,negated_conjecture,
~ ~ subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(s(n(e))),n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
subq(u(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(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(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(u(u(s(s(s(n(e)))),n(n(s(n(e))))),n(a(n(e),n(n(e))))),s(a(s(s(n(e))),n(n(e))))),u(a(u(s(s(s(n(e)))),n(n(s(n(e))))),a(n(e),n(n(e)))),a(s(n(n(e))),a(s(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(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),u(u(u(e,s(e)),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))))))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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)),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,[],[f58,f59,f59,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f54,f59,f59,f59]) ).
fof(f61,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f47]) ).
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(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),u(u(u(e,s(e)),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))))))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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)),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,[],[f60]) ).
tcf(c_75,plain,
mem(e,s(e)),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_101,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_56,c_51]) ).
tcf(c_137,plain,
! [X0: $i] :
( mem(X0,u(u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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)),s(u(e,s(e))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))))
| ~ mem(X0,u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),u(u(u(e,s(e)),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)))))))))) ),
inference(superposition,[status(thm)],[c_64,c_101]) ).
tcf(c_156,plain,
! [X0: $i] :
( mem(X0,u(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)))))))))
| mem(X0,u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),u(u(u(e,s(e)),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)))))))))) ),
inference(superposition,[status(thm)],[c_137,c_58]) ).
tcf(c_205,plain,
! [X0: $i] :
( mem(X0,u(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)))))))))
| mem(X0,u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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(u(u(e,s(e)),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))))))))) ),
inference(superposition,[status(thm)],[c_57,c_156]) ).
tcf(c_227,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)),s(u(e,s(e))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| ~ mem(X0,u(u(u(e,s(e)),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))))))))) ),
inference(superposition,[status(thm)],[c_205,c_58]) ).
tcf(c_270,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)),s(u(e,s(e))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_56,c_227]) ).
tcf(c_303,plain,
! [X0: $i] :
( mem(X0,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(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(X0,u(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)))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_270,c_58]) ).
tcf(c_324,plain,
! [X0: $i] :
( 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(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,s(u(s(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(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_303,c_58]) ).
tcf(c_360,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),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(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_324,c_58]) ).
tcf(c_390,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),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(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_360,c_55]) ).
tcf(c_428,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_390,c_55]) ).
tcf(c_461,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_56,c_428]) ).
tcf(c_507,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_461,c_55]) ).
tcf(c_531,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| 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))))))
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_507,c_58]) ).
tcf(c_575,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| 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 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_531,c_55]) ).
tcf(c_623,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| 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 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_575,c_55]) ).
tcf(c_669,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| ( s(u(e,s(e))) = X0 )
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_623,c_55]) ).
tcf(c_719,plain,
! [X0: $i] :
( ( u(e,s(e)) = X0 )
| ( s(u(e,s(e))) = X0 )
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_669,c_55]) ).
tcf(c_767,plain,
! [X0: $i] :
( ( u(e,s(e)) = X0 )
| ( s(u(e,s(e))) = X0 )
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(e)) ),
inference(superposition,[status(thm)],[c_57,c_719]) ).
tcf(c_844,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = e )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = e ) ),
inference(superposition,[status(thm)],[c_54,c_767]) ).
tcf(c_860,plain,
! [X0: $i] :
( mem(X0,e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = e )
| ~ mem(X0,s(s(u(e,s(e))))) ),
inference(superposition,[status(thm)],[c_844,c_56]) ).
tcf(c_9800,plain,
~ mem(e,e),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_9822,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_56,c_51]) ).
tcf(c_9856,plain,
! [X0: $i] :
( mem(X0,u(u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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)),s(u(e,s(e))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))))
| ~ mem(X0,u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),u(u(u(e,s(e)),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)))))))))) ),
inference(superposition,[status(thm)],[c_64,c_9822]) ).
tcf(c_9872,plain,
! [X0: $i] :
( mem(X0,u(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)))))))))
| mem(X0,u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))),u(u(u(e,s(e)),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)))))))))) ),
inference(superposition,[status(thm)],[c_9856,c_58]) ).
tcf(c_9918,plain,
! [X0: $i] :
( mem(X0,u(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)))))))))
| mem(X0,u(u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(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(u(u(e,s(e)),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))))))))) ),
inference(superposition,[status(thm)],[c_57,c_9872]) ).
tcf(c_9938,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)),s(u(e,s(e))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| ~ mem(X0,u(u(u(e,s(e)),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))))))))) ),
inference(superposition,[status(thm)],[c_9918,c_58]) ).
tcf(c_9974,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)),s(u(e,s(e))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(s(s(s(u(e,s(e))))),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_56,c_9938]) ).
tcf(c_10010,plain,
! [X0: $i] :
( mem(X0,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(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(X0,u(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)))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_9974,c_58]) ).
tcf(c_10029,plain,
! [X0: $i] :
( 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(u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,s(u(s(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(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_10010,c_58]) ).
tcf(c_10063,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),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(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_10029,c_58]) ).
tcf(c_10091,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),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(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_10063,c_55]) ).
tcf(c_10127,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(superposition,[status(thm)],[c_10091,c_55]) ).
tcf(c_10158,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_56,c_10127]) ).
tcf(c_10191,plain,
! [X0: $i] :
( mem(X0,s(s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10158,c_55]) ).
tcf(c_10219,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| 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))))))
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10191,c_58]) ).
tcf(c_10267,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| 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 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10219,c_55]) ).
tcf(c_10301,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| 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 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10267,c_55]) ).
tcf(c_10357,plain,
! [X0: $i] :
( mem(X0,s(u(e,s(e))))
| ( s(u(e,s(e))) = X0 )
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10301,c_55]) ).
tcf(c_10393,plain,
! [X0: $i] :
( ( u(e,s(e)) = X0 )
| ( s(u(e,s(e))) = X0 )
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10357,c_55]) ).
tcf(c_10441,plain,
! [X0: $i] :
( ( u(e,s(e)) = X0 )
| ( s(u(e,s(e))) = X0 )
| ( s(s(u(e,s(e)))) = X0 )
| ( u(u(e,s(e)),s(u(e,s(e)))) = X0 )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = X0 )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 )
| ~ mem(X0,s(e)) ),
inference(superposition,[status(thm)],[c_57,c_10393]) ).
tcf(c_10486,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = e )
| ( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = e ) ),
inference(superposition,[status(thm)],[c_54,c_10441]) ).
tcf(c_10502,plain,
! [X0: $i] :
( mem(X0,e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = e )
| ~ mem(X0,s(s(u(e,s(e))))) ),
inference(superposition,[status(thm)],[c_10486,c_56]) ).
tcf(c_10606,plain,
! [X0: $i] :
( ~ mem(X0,s(s(u(e,s(e)))))
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( s(u(e,s(e))) = e )
| ( u(e,s(e)) = e ) ),
inference(global_subsumption_just,[status(thm)],[c_10502,c_860,c_53]) ).
tcf(c_10607,plain,
! [X0: $i] :
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = e )
| ~ mem(X0,s(s(u(e,s(e))))) ),
inference(renaming,[status(thm)],[c_10606]) ).
tcf(c_10623,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(u(e,s(e)),s(u(e,s(e)))))) = e ) ),
inference(superposition,[status(thm)],[c_54,c_10607]) ).
tcf(c_10666,plain,
! [X0: $i] :
( mem(X0,e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10623,c_56]) ).
tcf(c_10683,plain,
! [X0: $i,X1: $i] :
( mem(X0,X1)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ~ subq(e,X1)
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_10623,c_9822]) ).
tcf(c_10845,plain,
! [X0: $i] :
( ~ mem(X0,u(e,s(e)))
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( s(u(e,s(e))) = e )
| ( u(e,s(e)) = e ) ),
inference(global_subsumption_just,[status(thm)],[c_10666,c_53,c_10666]) ).
tcf(c_10846,plain,
! [X0: $i] :
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ~ mem(X0,u(e,s(e))) ),
inference(renaming,[status(thm)],[c_10845]) ).
tcf(c_10861,plain,
! [X0: $i] :
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ~ mem(X0,s(e)) ),
inference(superposition,[status(thm)],[c_57,c_10846]) ).
tcf(c_10862,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ~ mem(e,s(e)) ),
inference(instantiation,[status(thm)],[c_10861]) ).
tcf(c_10863,plain,
( ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( s(u(e,s(e))) = e )
| ( u(e,s(e)) = e ) ),
inference(global_subsumption_just,[status(thm)],[c_10683,c_75,c_10862]) ).
tcf(c_10864,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( u(s(u(e,s(e))),s(s(u(e,s(e))))) = e ) ),
inference(renaming,[status(thm)],[c_10863]) ).
tcf(c_10876,plain,
! [X0: $i] :
( mem(X0,e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_10864,c_56]) ).
tcf(c_11159,plain,
! [X0: $i] :
( ~ mem(X0,s(u(e,s(e))))
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( s(u(e,s(e))) = e )
| ( u(e,s(e)) = e ) ),
inference(global_subsumption_just,[status(thm)],[c_10876,c_53,c_10876]) ).
tcf(c_11160,plain,
! [X0: $i] :
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(renaming,[status(thm)],[c_11159]) ).
tcf(c_11172,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ( u(u(e,s(e)),s(u(e,s(e)))) = e ) ),
inference(superposition,[status(thm)],[c_54,c_11160]) ).
tcf(c_11225,plain,
! [X0: $i] :
( mem(X0,e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ~ mem(X0,u(e,s(e))) ),
inference(superposition,[status(thm)],[c_11172,c_56]) ).
tcf(c_11226,plain,
! [X0: $i] :
( mem(X0,e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ~ mem(X0,s(u(e,s(e)))) ),
inference(superposition,[status(thm)],[c_11172,c_57]) ).
tcf(c_11277,plain,
! [X0: $i] :
( ~ mem(X0,u(e,s(e)))
| ( s(s(u(e,s(e)))) = e )
| ( s(u(e,s(e))) = e )
| ( u(e,s(e)) = e ) ),
inference(global_subsumption_just,[status(thm)],[c_11225,c_53,c_11225]) ).
tcf(c_11278,plain,
! [X0: $i] :
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ~ mem(X0,u(e,s(e))) ),
inference(renaming,[status(thm)],[c_11277]) ).
tcf(c_11289,plain,
! [X0: $i] :
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ~ mem(X0,s(e)) ),
inference(superposition,[status(thm)],[c_57,c_11278]) ).
tcf(c_11290,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e )
| ~ mem(e,s(e)) ),
inference(instantiation,[status(thm)],[c_11289]) ).
tcf(c_11291,plain,
( ( s(s(u(e,s(e)))) = e )
| ( s(u(e,s(e))) = e )
| ( u(e,s(e)) = e ) ),
inference(global_subsumption_just,[status(thm)],[c_11226,c_75,c_11290]) ).
tcf(c_11292,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e )
| ( s(s(u(e,s(e)))) = e ) ),
inference(renaming,[status(thm)],[c_11291]) ).
tcf(c_11301,plain,
( mem(s(u(e,s(e))),e)
| ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e ) ),
inference(superposition,[status(thm)],[c_11292,c_54]) ).
tcf(c_11447,plain,
( ( u(e,s(e)) = e )
| ( s(u(e,s(e))) = e ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11301,c_53]) ).
tcf(c_11454,plain,
( mem(u(e,s(e)),e)
| ( u(e,s(e)) = e ) ),
inference(superposition,[status(thm)],[c_11447,c_54]) ).
tcf(c_11869,plain,
u(e,s(e)) = e,
inference(forward_subsumption_resolution,[status(thm)],[c_11454,c_53]) ).
tcf(c_11872,plain,
! [X0: $i] :
( mem(X0,e)
| ~ mem(X0,s(e)) ),
inference(superposition,[status(thm)],[c_11869,c_57]) ).
tcf(c_11915,plain,
( mem(e,e)
| ~ mem(e,s(e)) ),
inference(instantiation,[status(thm)],[c_11872]) ).
tcf(c_11916,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11915,c_9800,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV572+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n026.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Thu Sep 24 15:04:30 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 10.71/7.76 % SZS status Started for theBenchmark.p
% 10.71/7.76 % SZS status Theorem for theBenchmark.p
% 10.71/7.76
% 10.71/7.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.71/7.76
% 10.71/7.76 % ------ iProver source info
% 10.71/7.76
% 10.71/7.76 % git: date: 2026-07-19 20:42:38 +0200
% 10.71/7.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.71/7.76 % git: non_committed_changes: false
% 10.71/7.76
% 10.71/7.76 % ------ Parsing...
% 10.71/7.76 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.71/7.76 % ------ Proving...
% 10.71/7.76 % ------ Problem Properties
% 10.71/7.76
% 10.71/7.76 %
% 10.71/7.76 % clauses 16
% 10.71/7.76 % conjectures 1
% 10.71/7.76 % EPR 3
% 10.71/7.76 % Horn 13
% 10.71/7.76 % unary 3
% 10.71/7.76 % binary 9
% 10.71/7.76 % lits 33
% 10.71/7.76 % lits eq 2
% 10.71/7.76 % fd_pure 0
% 10.71/7.76 % fd_pseudo 0
% 10.71/7.76 % fd_cond 0
% 10.71/7.76 % fd_pseudo_cond 2
% 10.71/7.76 % AC symbols 0
% 10.71/7.76
% 10.71/7.76 % ------ Input Options Time Limit: Unbounded
% 10.71/7.76
% 10.71/7.76
% 10.71/7.76 % ------
% 10.71/7.76 % Current options:
% 10.71/7.76 % ------
% 10.71/7.76
% 10.71/7.76
% 10.71/7.76 %
% 10.71/7.76
% 10.71/7.76 % ------ Proving...
% 10.71/7.76 %
% 10.71/7.76
% 10.71/7.76 % ------ Proving...
% 10.71/7.76 %
% 10.71/7.76
% 10.71/7.76 % SZS status Theorem for theBenchmark.p
% 10.71/7.76
% 10.71/7.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.71/7.77
% 10.71/7.77
%------------------------------------------------------------------------------