%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV562+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 : n011.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 3.66s 1.12s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 147 ( 58 unt; 17 def)
% Number of atoms : 457 ( 60 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 257 ( 108 ~; 117 |; 21 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 18 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 178 ( 0 sgn 173 !; 5 ?; 74 :)
% 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(f2,axiom,
! [X0,X1] :
( subq(X0,X1)
=> ( subq(X1,X0)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',setext) ).
fof(f3,axiom,
! [X0,X1] :
( disj(X0,X1)
<=> ~ ? [X2] :
( mem(X2,X1)
& mem(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',disj_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(f7,axiom,
! [X0,X1,X2] :
( mem(X0,m(X1,X2))
<=> ( ~ mem(X0,X2)
& mem(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',m_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(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',p_ax) ).
fof(f26,conjecture,
disj(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(s(n(e))),n(n(e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disj_4914_8333) ).
fof(f27,negated_conjecture,
~ disj(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(s(n(e))),n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ disj(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(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(f31,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| ~ subq(X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| ~ subq(X1,X0)
| X0 = X1 ),
inference(flattening,[],[f31]) ).
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(f41,plain,
! [X0,X1,X2] :
( ( ~ mem(X0,m(X1,X2))
| ( ~ mem(X0,X2)
& mem(X0,X1) ) )
& ( mem(X0,X2)
| ~ mem(X0,X1)
| mem(X0,m(X1,X2)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ~ mem(X0,m(X1,X2))
| ( ~ mem(X0,X2)
& mem(X0,X1) ) )
& ( mem(X0,X2)
| ~ mem(X0,X1)
| mem(X0,m(X1,X2)) ) ),
inference(flattening,[],[f41]) ).
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(f45,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f46,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| ~ subq(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f32]) ).
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(f56,plain,
! [X2,X0,X1] :
( ~ mem(X0,m(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ mem(X0,m(X1,X2))
| mem(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
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(m(p(a(p(s(n(e))),n(n(e)))),n(a(p(s(n(e))),n(n(e))))),u(s(u(n(e),n(s(n(e))))),n(a(p(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(m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(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(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),
inference(definition_unfolding,[],[f63,f59,f64,f64,f64,f64,f59,f64,f64,f64,f64,f64,f64,f64,f59,f64,f64,f64]) ).
fof(f66,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f52]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| ~ mem(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subq(X0,X1)
| mem(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
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_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
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_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,X1)
| ~ mem(X0,m(X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ mem(X0,X2)
| ~ mem(X0,m(X1,X2)) ),
inference(cnf_transformation,[],[f56]) ).
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(m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(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(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(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_295,plain,
! [X0: $i,X1: $i] :
( mem(sK1(X0,X1),X1)
| ( u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) != X1 )
| ( m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_66]) ).
tcf(c_296,plain,
mem(sK1(m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(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(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(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(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),
inference(unflattening,[status(thm)],[c_295]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] :
( mem(sK1(X0,X1),X0)
| ( u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) != X1 )
| ( m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_107,c_66]) ).
tcf(c_301,plain,
mem(sK1(m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(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(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),m(p(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))),u(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(p(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),
inference(unflattening,[status(thm)],[c_300]) ).
tcf(c_500,definition,
iPr_def_10 = s(e),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_501,definition,
iPr_def_11 = u(e,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_502,definition,
iPr_def_12 = s(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_503,definition,
iPr_def_13 = p(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_504,definition,
iPr_def_14 = u(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_505,definition,
iPr_def_15 = s(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_506,definition,
iPr_def_16 = u(iPr_def_13,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_507,definition,
iPr_def_17 = p(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_508,definition,
iPr_def_18 = s(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_509,definition,
iPr_def_19 = u(iPr_def_16,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_510,definition,
iPr_def_20 = m(iPr_def_17,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_511,definition,
iPr_def_21 = s(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_512,definition,
iPr_def_22 = u(iPr_def_12,iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_513,definition,
iPr_def_23 = u(iPr_def_11,iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_514,definition,
iPr_def_24 = s(iPr_def_23),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_515,definition,
iPr_def_25 = u(iPr_def_24,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_516,definition,
iPr_def_26 = sK1(iPr_def_20,iPr_def_25),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_517,plain,
mem(iPr_def_26,iPr_def_20),
inference(demodulation,[status(thm)],[c_301,c_511,c_512,c_513,c_514,c_515,c_508,c_509,c_504,c_505,c_500,c_501,c_502,c_503,c_506,c_507,c_510,c_516]) ).
tcf(c_518,plain,
mem(iPr_def_26,iPr_def_25),
inference(demodulation,[status(thm)],[c_296]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( mem(X0,X2)
| ~ mem(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1014,plain,
mem(e,iPr_def_10),
inference(superposition,[status(thm)],[c_500,c_56]) ).
tcf(c_1015,plain,
mem(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_502,c_56]) ).
tcf(c_1042,plain,
! [X0: $i] :
( subq(X0,iPr_def_12)
| ~ mem(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_503,c_65]) ).
tcf(c_1043,plain,
! [X0: $i] :
( subq(X0,iPr_def_16)
| ~ mem(X0,iPr_def_17) ),
inference(superposition,[status(thm)],[c_507,c_65]) ).
tcf(c_1124,plain,
! [X0: $i] :
( ( X0 = e )
| ~ mem(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_500,c_57]) ).
tcf(c_1125,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ~ mem(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_502,c_57]) ).
tcf(c_1126,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ~ mem(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_505,c_57]) ).
tcf(c_1129,plain,
! [X0: $i] :
( ( X0 = iPr_def_23 )
| ~ mem(X0,iPr_def_24) ),
inference(superposition,[status(thm)],[c_514,c_57]) ).
tcf(c_1158,plain,
! [X0: $i] :
( mem(X0,iPr_def_22)
| ~ mem(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_512,c_58]) ).
tcf(c_1187,plain,
! [X0: $i] :
( mem(X0,iPr_def_11)
| ~ mem(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_501,c_59]) ).
tcf(c_1188,plain,
! [X0: $i] :
( mem(X0,iPr_def_14)
| ~ mem(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_504,c_59]) ).
tcf(c_1192,plain,
! [X0: $i] :
( mem(X0,iPr_def_23)
| ~ mem(X0,iPr_def_22) ),
inference(superposition,[status(thm)],[c_513,c_59]) ).
tcf(c_1231,plain,
! [X0: $i] :
( mem(X0,iPr_def_17)
| ~ mem(X0,iPr_def_20) ),
inference(superposition,[status(thm)],[c_510,c_62]) ).
tcf(c_1290,plain,
mem(iPr_def_11,iPr_def_22),
inference(superposition,[status(thm)],[c_1015,c_1158]) ).
tcf(c_1318,plain,
! [X0: $i] :
( ~ mem(X0,iPr_def_20)
| ~ mem(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_510,c_63]) ).
tcf(c_1346,plain,
! [X0: $i] :
( mem(e,X0)
| ~ subq(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_1014,c_51]) ).
tcf(c_1504,plain,
! [X0: $i] :
( mem(X0,iPr_def_10)
| mem(X0,e)
| ~ mem(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_501,c_60]) ).
tcf(c_1506,plain,
! [X0: $i] :
( mem(X0,iPr_def_15)
| mem(X0,iPr_def_13)
| ~ mem(X0,iPr_def_16) ),
inference(superposition,[status(thm)],[c_506,c_60]) ).
tcf(c_1510,plain,
! [X0: $i] :
( mem(X0,iPr_def_24)
| mem(X0,iPr_def_19)
| ~ mem(X0,iPr_def_25) ),
inference(superposition,[status(thm)],[c_515,c_60]) ).
tcf(c_1529,plain,
! [X0: $i] :
( mem(X0,iPr_def_10)
| ~ mem(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1504,c_55]) ).
tcf(c_1577,plain,
! [X0: $i] :
( subq(iPr_def_10,X0)
| mem(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_50,c_1187]) ).
tcf(c_1624,plain,
mem(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_1015,c_1188]) ).
tcf(c_1754,plain,
mem(iPr_def_11,iPr_def_23),
inference(superposition,[status(thm)],[c_1290,c_1192]) ).
tcf(c_1803,plain,
! [X0: $i] :
( mem(iPr_def_11,X0)
| ~ subq(iPr_def_23,X0) ),
inference(superposition,[status(thm)],[c_1754,c_51]) ).
tcf(c_1907,plain,
mem(iPr_def_26,iPr_def_17),
inference(superposition,[status(thm)],[c_517,c_1231]) ).
tcf(c_1946,plain,
subq(iPr_def_26,iPr_def_16),
inference(superposition,[status(thm)],[c_1907,c_1043]) ).
tcf(c_2071,plain,
! [X0: $i] :
( subq(iPr_def_11,X0)
| mem(sK0(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_1529]) ).
tcf(c_2467,plain,
subq(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1577,c_49]) ).
tcf(c_2710,plain,
subq(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_2071,c_49]) ).
tcf(c_2751,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subq(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2710,c_52]) ).
tcf(c_2753,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_2751,c_2467]) ).
tcf(c_2762,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ mem(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_1125,c_2753]) ).
tcf(c_2763,plain,
! [X0: $i] :
( mem(iPr_def_10,X0)
| ~ subq(iPr_def_23,X0) ),
inference(demodulation,[status(thm)],[c_1803,c_2753]) ).
tcf(c_2770,plain,
mem(iPr_def_10,iPr_def_14),
inference(demodulation,[status(thm)],[c_1624,c_2753]) ).
tcf(c_2799,plain,
( ( e = iPr_def_10 )
| ~ mem(e,iPr_def_12) ),
inference(instantiation,[status(thm)],[c_2762]) ).
tcf(c_3732,plain,
! [X0: $i,X1: $i,X2: $i] :
( mem(X0,X2)
| ~ mem(X1,iPr_def_10)
| ( X2 != iPr_def_10 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_522]) ).
tcf(c_3733,plain,
( mem(e,e)
| ~ mem(e,iPr_def_10)
| ( e != iPr_def_10 )
| ( e != e ) ),
inference(instantiation,[status(thm)],[c_3732]) ).
tcf(c_4450,plain,
( mem(iPr_def_26,iPr_def_24)
| mem(iPr_def_26,iPr_def_19) ),
inference(superposition,[status(thm)],[c_518,c_1510]) ).
tcf(c_4577,plain,
( mem(iPr_def_26,iPr_def_19)
| ( iPr_def_23 = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_4450,c_1129]) ).
tcf(c_4611,plain,
( ( iPr_def_23 = iPr_def_26 )
| ~ mem(iPr_def_26,iPr_def_20) ),
inference(superposition,[status(thm)],[c_4577,c_1318]) ).
tcf(c_4613,plain,
iPr_def_23 = iPr_def_26,
inference(forward_subsumption_resolution,[status(thm)],[c_4611,c_517]) ).
tcf(c_4617,plain,
subq(iPr_def_23,iPr_def_16),
inference(demodulation,[status(thm)],[c_1946,c_4613]) ).
tcf(c_4636,plain,
mem(iPr_def_10,iPr_def_16),
inference(superposition,[status(thm)],[c_4617,c_2763]) ).
tcf(c_4987,plain,
( mem(iPr_def_10,iPr_def_15)
| mem(iPr_def_10,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4636,c_1506]) ).
tcf(c_5078,plain,
( mem(iPr_def_10,iPr_def_13)
| ( iPr_def_10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4987,c_1126]) ).
tcf(c_5117,plain,
( subq(iPr_def_10,iPr_def_12)
| ( iPr_def_10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5078,c_1042]) ).
tcf(c_5247,plain,
( mem(e,iPr_def_12)
| ( iPr_def_10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5117,c_1346]) ).
tcf(c_5253,plain,
iPr_def_10 = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_5247,c_67,c_68,c_74,c_1014,c_2799,c_3733,c_5247]) ).
tcf(c_5263,plain,
mem(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_2770,c_5253]) ).
tcf(c_5349,plain,
e = iPr_def_10,
inference(superposition,[status(thm)],[c_5263,c_1124]) ).
tcf(c_5378,plain,
! [X0: $i] : ~ mem(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_55,c_5349]) ).
tcf(c_5379,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_5263,c_5378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV562+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Thu Sep 24 15:00:13 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 3.66/1.12 % SZS status Started for theBenchmark.p
% 3.66/1.12 % SZS status Theorem for theBenchmark.p
% 3.66/1.12
% 3.66/1.12 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.66/1.12
% 3.66/1.12 % ------ iProver source info
% 3.66/1.12
% 3.66/1.12 % git: date: 2026-07-19 20:42:38 +0200
% 3.66/1.12 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.66/1.12 % git: non_committed_changes: false
% 3.66/1.12
% 3.66/1.12 % ------ Parsing...
% 3.66/1.12 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.66/1.12
% 3.66/1.12 % ------ 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 %
% 3.66/1.12
% 3.66/1.12 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.66/1.12
% 3.66/1.12 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.66/1.12 % ------ Proving...
% 3.66/1.12 % ------ Problem Properties
% 3.66/1.12
% 3.66/1.12 %
% 3.66/1.12 % clauses 34
% 3.66/1.12 % conjectures 0
% 3.66/1.12 % EPR 5
% 3.66/1.12 % Horn 31
% 3.66/1.12 % unary 21
% 3.66/1.12 % binary 9
% 3.66/1.12 % lits 51
% 3.66/1.12 % lits eq 19
% 3.66/1.12 % fd_pure 0
% 3.66/1.12 % fd_pseudo 0
% 3.66/1.12 % fd_cond 0
% 3.66/1.12 % fd_pseudo_cond 2
% 3.66/1.12 % AC symbols 0
% 3.66/1.12
% 3.66/1.12 % ------ Schedule dynamic 5 is on
% 3.66/1.12
% 3.66/1.12 % ------ no conjectures: strip conj schedule
% 3.66/1.12
% 3.66/1.12 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.66/1.12
% 3.66/1.12
% 3.66/1.12 % ------
% 3.66/1.12 % Current options:
% 3.66/1.12 % ------
% 3.66/1.12
% 3.66/1.12
% 3.66/1.12 %
% 3.66/1.12
% 3.66/1.12 % ------ Proving...
% 3.66/1.12 %
% 3.66/1.12
% 3.66/1.12 % SZS status Theorem for theBenchmark.p
% 3.66/1.12
% 3.66/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.66/1.12
% 3.66/1.12
%------------------------------------------------------------------------------