%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV582+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 : n015.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 03:02:48 PM UTC 2026
% Result : Theorem 5.00s 1.74s
% Output : CNFRefutation 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 23 unt; 0 def)
% Number of atoms : 126 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 52 ~; 52 |; 11 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 13 ( 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 : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 84 !; 2 ?; 28 :)
% 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(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(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(s(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subq_402_33170) ).
fof(f27,negated_conjecture,
~ subq(u(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(s(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ subq(u(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(s(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(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] :
( ( ~ mem(X0,s(X1))
| X0 = X1 )
& ( X0 != X1
| mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f33,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(f34,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,[],[f33]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f38,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))],[f37]) ).
fof(f39,plain,
~ subq(u(a(a(s(n(e)),s(s(n(e)))),u(n(e),n(s(n(e))))),s(s(n(n(e))))),u(u(s(u(n(e),n(s(n(e))))),a(s(s(s(n(e)))),s(n(n(e))))),a(s(n(e)),p(n(n(e)))))),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f43,plain,
! [X0,X1] :
( X0 != X1
| mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ mem(X0,X2)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ mem(X0,X1)
| mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f47,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f50,plain,
! [X3,X0,X1] :
( ~ subq(X0,X1)
| ~ mem(X3,X0)
| mem(X3,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f51,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f52,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f54,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f47,f41]) ).
fof(f55,plain,
~ subq(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(definition_unfolding,[],[f39,f41,f41,f54,f54,f54,f54,f54,f54,f54,f54,f54,f54,f41,f54,f54,f54,f41,f54,f54,f54]) ).
fof(f56,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f43]) ).
tcf(c_49,negated_conjecture,
~ subq(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(cnf_transformation,[],[f55]) ).
tcf(c_51,plain,
! [X0: $i] : mem(X0,s(X0)),
inference(cnf_transformation,[],[f56]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ mem(X0,s(X1)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,u(X2,X1))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,X2)
| mem(X0,X1)
| ~ mem(X0,u(X1,X2)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ mem(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| mem(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X2,X1)
| ~ mem(X2,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i] :
( subq(s(X0),X1)
| ( sK0(s(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_59,c_52]) ).
tcf(c_618,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,X2)
| ( sK0(s(X1),X2) = X1 )
| ~ mem(X0,s(X1)) ),
inference(superposition,[status(thm)],[c_569,c_60]) ).
tcf(c_763,plain,
( subq(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_768,plain,
( subq(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_794,plain,
! [X0: $i,X1: $i] :
( mem(X0,X1)
| ( sK0(s(X0),X1) = X0 ) ),
inference(superposition,[status(thm)],[c_51,c_618]) ).
tcf(c_811,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ( sK0(s(sK0(X0,X1)),X1) = sK0(X0,X1) ) ),
inference(superposition,[status(thm)],[c_794,c_58]) ).
tcf(c_848,plain,
( mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| ~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_942,plain,
sK0(s(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e)))))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))) = sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(superposition,[status(thm)],[c_811,c_49]) ).
tcf(c_1001,plain,
( subq(s(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e)))))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(superposition,[status(thm)],[c_942,c_58]) ).
tcf(c_1487,plain,
( mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(s(u(e,s(e))),s(s(s(u(e,s(e)))))))
| mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| ~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1505,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(global_subsumption_just,[status(thm)],[c_1001,c_49,c_763]) ).
tcf(c_1507,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(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(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(superposition,[status(thm)],[c_53,c_1505]) ).
tcf(c_1513,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e)))))))),
inference(superposition,[status(thm)],[c_54,c_1505]) ).
tcf(c_1518,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(u(e,s(e)))),
inference(superposition,[status(thm)],[c_53,c_1513]) ).
tcf(c_1540,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),
inference(superposition,[status(thm)],[c_53,c_1507]) ).
tcf(c_1546,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),
inference(superposition,[status(thm)],[c_54,c_1507]) ).
tcf(c_2701,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(s(s(u(e,s(e)))))),
inference(superposition,[status(thm)],[c_53,c_1546]) ).
tcf(c_2709,plain,
~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),
inference(superposition,[status(thm)],[c_54,c_1546]) ).
tcf(c_4026,plain,
( mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(u(e,s(e))))
| mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),s(s(s(u(e,s(e))))))
| ~ mem(sK0(u(u(u(s(u(e,s(e))),s(s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(s(s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(e,s(e))),s(p(u(u(e,s(e)),s(u(e,s(e))))))))),u(s(u(e,s(e))),s(s(s(u(e,s(e))))))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_4027,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4026,c_2709,c_2701,c_1540,c_1518,c_1487,c_848,c_768,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV582+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.65 % Computer : n015.cluster.edu
% 0.16/0.65 % Model : x86_64 x86_64
% 0.16/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.65 % Memory : 8046.5625MB
% 0.16/0.65 % OS : Linux 6.8.0-71-generic
% 0.16/0.65 % CPULimit : 300
% 0.16/0.65 % WCLimit : 300
% 0.16/0.65 % DateTime : Thu Sep 24 15:06:27 UTC 2026
% 0.16/0.65 % CPUTime :
% 0.16/0.65 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.21/0.71 Running first-order theorem proving
% 0.21/0.71 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
% 0.21/0.72
% 0.21/0.72 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.72
% 0.21/0.73 % Detected problem language: tptp
% 0.21/0.75 % Proving...
% 5.00/1.74 % SZS status Started for theBenchmark.p
% 5.00/1.74 % SZS status Theorem for theBenchmark.p
% 5.00/1.74
% 5.00/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.00/1.74
% 5.00/1.74 % ------ iProver source info
% 5.00/1.74
% 5.00/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 5.00/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.00/1.74 % git: non_committed_changes: false
% 5.00/1.74
% 5.00/1.74 % ------ Parsing...
% 5.00/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.00/1.74
% 5.00/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 5.00/1.74
% 5.00/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.00/1.74
% 5.00/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.00/1.74 % ------ Proving...
% 5.00/1.74 % ------ Problem Properties
% 5.00/1.74
% 5.00/1.74 %
% 5.00/1.74 % clauses 13
% 5.00/1.74 % conjectures 1
% 5.00/1.74 % EPR 3
% 5.00/1.74 % Horn 11
% 5.00/1.74 % unary 3
% 5.00/1.74 % binary 7
% 5.00/1.74 % lits 26
% 5.00/1.74 % lits eq 2
% 5.00/1.74 % fd_pure 0
% 5.00/1.74 % fd_pseudo 0
% 5.00/1.74 % fd_cond 0
% 5.00/1.74 % fd_pseudo_cond 2
% 5.00/1.74 % AC symbols 0
% 5.00/1.74
% 5.00/1.74 % ------ Schedule dynamic 5 is on
% 5.00/1.74
% 5.00/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.00/1.74
% 5.00/1.74
% 5.00/1.74 % ------
% 5.00/1.74 % Current options:
% 5.00/1.74 % ------
% 5.00/1.74
% 5.00/1.74
% 5.00/1.74 %
% 5.00/1.74
% 5.00/1.74 % ------ Proving...
% 5.00/1.74 %
% 5.00/1.74
% 5.00/1.74 % SZS status Theorem for theBenchmark.p
% 5.00/1.74
% 5.00/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.00/1.74
% 5.00/1.74
%------------------------------------------------------------------------------