%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU256+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:56:23 PM UTC 2026
% Result : Theorem 4.61s 7.22s
% Output : CNFRefutation 4.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 105 ( 16 unt; 1 def)
% Number of atoms : 354 ( 23 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 374 ( 157 ~; 160 |; 43 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 199 ( 0 sgn 187 !; 12 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> ! [X1] :
~ ( ! [X2] :
~ ( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
& X1 != empty_set
& subset(X1,relation_field(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f14,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f36,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f37,axiom,
! [X0,X1,X2] :
( relation(X2)
=> subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f43,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f44,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f45,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f52,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] :
( in(X3,X1)
& in(X3,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f43]) ).
fof(f59,plain,
! [X0] :
( ~ relation(X0)
| ( well_founded_relation(X0)
<=> ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ relation(X1)
| ( subset(relation_field(relation_restriction(X1,X0)),X0)
& subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f71,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f72,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0,X1] :
( relation(X1)
& well_founded_relation(X1)
& ~ well_founded_relation(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f41]) ).
fof(f74,plain,
? [X0,X1] :
( relation(X1)
& well_founded_relation(X1)
& ~ well_founded_relation(relation_restriction(X1,X0)) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ? [X2] :
( in(X2,X1)
& in(X2,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f82,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X1] :
( ? [X2] :
( disjoint(fiber(X0,X2),X1)
& in(X2,X1) )
| empty_set = X1
| ~ subset(X1,relation_field(X0)) ) )
& ( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f83,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ? [X4] :
( disjoint(fiber(X0,X4),X3)
& in(X4,X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ? [X1] :
( ! [X2] :
( ~ disjoint(fiber(X0,X2),X1)
| ~ in(X2,X1) )
& empty_set != X1
& subset(X1,relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ( disjoint(fiber(X0,sK1(X0,X3)),X3)
& in(sK1(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK0(X0))
| ~ in(X2,sK0(X0)) )
& empty_set != sK0(X0)
& subset(sK0(X0),relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X4,sK1(X0,X3))],[f83]) ).
fof(f91,plain,
( relation(sK9)
& well_founded_relation(sK9)
& ~ well_founded_relation(relation_restriction(sK9,sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f74]) ).
fof(f92,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f93,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X0) ) )
& ( ( in(sK10(X0,X1),X1)
& in(sK10(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f75]) ).
fof(f100,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| disjoint(fiber(X0,sK1(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f101,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| in(sK1(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f102,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X2),sK0(X0))
| ~ in(X2,sK0(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f103,plain,
! [X0] :
( ~ relation(X0)
| empty_set != sK0(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f104,plain,
! [X0] :
( ~ relation(X0)
| subset(sK0(X0),relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f107,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f129,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f132,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f133,plain,
relation(sK9),
inference(cnf_transformation,[],[f91]) ).
fof(f134,plain,
well_founded_relation(sK9),
inference(cnf_transformation,[],[f91]) ).
fof(f135,plain,
~ well_founded_relation(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f91]) ).
fof(f137,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f138,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f139,plain,
! [X0,X1] :
( in(sK10(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f140,plain,
! [X0,X1] :
( in(sK10(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_53,plain,
! [X0: $i] :
( well_founded_relation(X0)
| subset(sK0(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_54,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ( sK0(X0) != empty_set ) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ in(X1,sK0(X0))
| ~ disjoint(fiber(X0,X1),sK0(X0)) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(sK1(X1,X0),X0)
| ( X0 = empty_set )
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X1,sK1(X1,X0)),X0)
| ( X0 = empty_set )
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(fiber(relation_restriction(X0,X1),X2),fiber(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_86,negated_conjecture,
~ well_founded_relation(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f135]) ).
tcf(c_87,negated_conjecture,
well_founded_relation(sK9),
inference(cnf_transformation,[],[f134]) ).
tcf(c_88,negated_conjecture,
relation(sK9),
inference(cnf_transformation,[],[f133]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X2,X1)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_94,c_125]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_95,c_125]) ).
tcf(c_1686,definition,
iPr_def_10 = relation_restriction(sK9,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1687,negated_conjecture,
relation(sK9),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_1688,negated_conjecture,
well_founded_relation(sK9),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1689,negated_conjecture,
~ well_founded_relation(iPr_def_10),
inference(demodulation,[status(thm)],[c_86,c_1686]) ).
tcf(c_2559,plain,
( relation(iPr_def_10)
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1686,c_60]) ).
tcf(c_2560,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2559,c_1687]) ).
tcf(c_2737,plain,
( subset(relation_field(iPr_def_10),relation_field(sK9))
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1686,c_81]) ).
tcf(c_2738,plain,
subset(relation_field(iPr_def_10),relation_field(sK9)),
inference(forward_subsumption_resolution,[status(thm)],[c_2737,c_1687]) ).
tcf(c_2795,plain,
! [X0: $i] :
( subset(X0,relation_field(sK9))
| ~ subset(X0,relation_field(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_2738,c_80]) ).
tcf(c_2852,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X1)
| ~ disjoint(X2,X1)
| ~ in(sK10(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_92,c_93]) ).
tcf(c_2880,plain,
! [X0: $i] :
( subset(fiber(iPr_def_10,X0),fiber(sK9,X0))
| ~ relation(sK9) ),
inference(superposition,[status(thm)],[c_1686,c_83]) ).
tcf(c_2882,plain,
! [X0: $i] : subset(fiber(iPr_def_10,X0),fiber(sK9,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2880,c_1687]) ).
tcf(c_2965,plain,
! [X0: $i,X1: $i] :
( in(sK1(X1,sK0(X0)),sK0(X0))
| ( sK0(X0) = empty_set )
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(sK0(X0),relation_field(X1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_3003,plain,
( well_founded_relation(iPr_def_10)
| subset(sK0(iPr_def_10),relation_field(sK9))
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_53,c_2795]) ).
tcf(c_3011,plain,
subset(sK0(iPr_def_10),relation_field(sK9)),
inference(forward_subsumption_resolution,[status(thm)],[c_3003,c_1689,c_2560]) ).
tcf(c_3184,plain,
! [X0: $i] :
( in(sK1(sK9,sK0(X0)),sK0(X0))
| ( sK0(X0) = empty_set )
| ~ relation(sK9)
| ~ well_founded_relation(sK9)
| ~ subset(sK0(X0),relation_field(sK9)) ),
inference(instantiation,[status(thm)],[c_2965]) ).
tcf(c_3626,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| element(sK10(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_91,c_259]) ).
tcf(c_4050,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ empty(X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_91,c_260]) ).
tcf(c_7574,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| disjoint(X0,X2)
| in(sK10(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3626,c_85]) ).
tcf(c_16629,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X0,X1)
| in(sK10(X0,X2),X1)
| disjoint(X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_7574,c_4050,c_7574]) ).
tcf(c_16630,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| in(sK10(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_16629]) ).
tcf(c_16646,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_16630,c_2852]) ).
tcf(c_32279,plain,
( in(sK1(sK9,sK0(iPr_def_10)),sK0(iPr_def_10))
| ( sK0(iPr_def_10) = empty_set )
| ~ relation(sK9)
| ~ well_founded_relation(sK9)
| ~ subset(sK0(iPr_def_10),relation_field(sK9)) ),
inference(instantiation,[status(thm)],[c_3184]) ).
tcf(c_38650,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(iPr_def_10,X0),X1)
| ~ disjoint(fiber(sK9,X0),X1) ),
inference(superposition,[status(thm)],[c_2882,c_16646]) ).
tcf(c_40160,plain,
! [X0: $i] :
( disjoint(fiber(iPr_def_10,sK1(sK9,X0)),X0)
| ( X0 = empty_set )
| ~ relation(sK9)
| ~ well_founded_relation(sK9)
| ~ subset(X0,relation_field(sK9)) ),
inference(superposition,[status(thm)],[c_57,c_38650]) ).
tcf(c_40214,plain,
! [X0: $i] :
( disjoint(fiber(iPr_def_10,sK1(sK9,X0)),X0)
| ( X0 = empty_set )
| ~ subset(X0,relation_field(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40160,c_1687,c_1688]) ).
tcf(c_40224,plain,
( well_founded_relation(iPr_def_10)
| ( sK0(iPr_def_10) = empty_set )
| ~ relation(iPr_def_10)
| ~ subset(sK0(iPr_def_10),relation_field(sK9))
| ~ in(sK1(sK9,sK0(iPr_def_10)),sK0(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_40214,c_55]) ).
tcf(c_40279,plain,
( ( sK0(iPr_def_10) = empty_set )
| ~ in(sK1(sK9,sK0(iPr_def_10)),sK0(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40224,c_1689,c_2560,c_3011]) ).
tcf(c_40394,plain,
sK0(iPr_def_10) = empty_set,
inference(global_subsumption_just,[status(thm)],[c_40279,c_88,c_87,c_3011,c_32279,c_40279]) ).
tcf(c_40573,plain,
( well_founded_relation(iPr_def_10)
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_40394,c_54]) ).
tcf(c_40576,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_40573,c_1689,c_2560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU256+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n017.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Thu Sep 24 13:20:52 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 4.61/7.22 % SZS status Started for theBenchmark.p
% 4.61/7.22 % SZS status Theorem for theBenchmark.p
% 4.61/7.22
% 4.61/7.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.61/7.22
% 4.61/7.22 % ------ iProver source info
% 4.61/7.22
% 4.61/7.22 % git: date: 2026-07-19 20:42:38 +0200
% 4.61/7.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.61/7.22 % git: non_committed_changes: false
% 4.61/7.22
% 4.61/7.22 % ------ Parsing...
% 4.61/7.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.61/7.22
% 4.61/7.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.61/7.22
% 4.61/7.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.61/7.22
% 4.61/7.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.61/7.22 % ------ Proving...
% 4.61/7.22 % ------ Problem Properties
% 4.61/7.22
% 4.61/7.22 %
% 4.61/7.22 % clauses 47
% 4.61/7.22 % conjectures 3
% 4.61/7.22 % EPR 22
% 4.61/7.22 % Horn 41
% 4.61/7.22 % unary 19
% 4.61/7.22 % binary 17
% 4.61/7.22 % lits 91
% 4.61/7.22 % lits eq 14
% 4.61/7.22 % fd_pure 0
% 4.61/7.22 % fd_pseudo 0
% 4.61/7.22 % fd_cond 3
% 4.61/7.22 % fd_pseudo_cond 1
% 4.61/7.22 % AC symbols 0
% 4.61/7.22
% 4.61/7.22 % ------ Schedule dynamic 5 is on
% 4.61/7.22
% 4.61/7.22 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.61/7.22
% 4.61/7.22
% 4.61/7.22 % ------
% 4.61/7.22 % Current options:
% 4.61/7.22 % ------
% 4.61/7.22
% 4.61/7.22
% 4.61/7.22 %
% 4.61/7.22
% 4.61/7.22 % ------ Proving...
% 4.61/7.22 %
% 4.61/7.22
% 4.61/7.22 % SZS status Theorem for theBenchmark.p
% 4.61/7.22
% 4.61/7.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.61/7.22
% 4.61/7.22
%------------------------------------------------------------------------------