%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU256+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 65.26s 19.95s
% Output : CNFRefutation 65.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 17 unt; 1 def)
% Number of atoms : 241 ( 22 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 236 ( 99 ~; 99 |; 26 &)
% ( 2 <=>; 10 =>; 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 : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 99 !; 9 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f37,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/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f85,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f214,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f217,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/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
fof(f221,axiom,
! [X0,X1,X2] :
( relation(X2)
=> subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_wellord1) ).
fof(f239,conjecture,
! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
fof(f240,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( well_founded_relation(X1)
=> well_founded_relation(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f239]) ).
fof(f287,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f361,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,[],[f37]) ).
fof(f394,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f85]) ).
fof(f507,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f214]) ).
fof(f508,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f507]) ).
fof(f511,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,[],[f217]) ).
fof(f517,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(ennf_transformation,[],[f221]) ).
fof(f544,plain,
? [X0,X1] :
( relation(X1)
& well_founded_relation(X1)
& ~ well_founded_relation(relation_restriction(X1,X0)) ),
inference(ennf_transformation,[],[f240]) ).
fof(f545,plain,
? [X0,X1] :
( relation(X1)
& well_founded_relation(X1)
& ~ well_founded_relation(relation_restriction(X1,X0)) ),
inference(flattening,[],[f544]) ).
fof(f596,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(ennf_transformation,[],[f287]) ).
fof(f597,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(flattening,[],[f596]) ).
fof(f697,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,[],[f361]) ).
fof(f698,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,[],[f697]) ).
fof(f699,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_founded_relation(X0)
| ! [X3] :
( ( disjoint(fiber(X0,sK34(X0,X3)),X3)
& in(sK34(X0,X3),X3) )
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ) )
& ( ( ! [X2] :
( ~ disjoint(fiber(X0,X2),sK33(X0))
| ~ in(X2,sK33(X0)) )
& empty_set != sK33(X0)
& subset(sK33(X0),relation_field(X0)) )
| well_founded_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33,sK34]),skolemize(X1,sK33(X0)),skolemize(X4,sK34(X0,X3))],[f698]) ).
fof(f826,plain,
( relation(sK108)
& well_founded_relation(sK108)
& ~ well_founded_relation(relation_restriction(sK108,sK107)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107,sK108]),skolemize(X0,sK107),skolemize(X1,sK108)],[f545]) ).
fof(f998,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| disjoint(fiber(X0,sK34(X0,X3)),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f699]) ).
fof(f999,plain,
! [X3,X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| in(sK34(X0,X3),X3)
| empty_set = X3
| ~ subset(X3,relation_field(X0)) ),
inference(cnf_transformation,[],[f699]) ).
fof(f1000,plain,
! [X2,X0] :
( ~ relation(X0)
| ~ disjoint(fiber(X0,X2),sK33(X0))
| ~ in(X2,sK33(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f699]) ).
fof(f1001,plain,
! [X0] :
( ~ relation(X0)
| empty_set != sK33(X0)
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f699]) ).
fof(f1002,plain,
! [X0] :
( ~ relation(X0)
| subset(sK33(X0),relation_field(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f699]) ).
fof(f1140,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f394]) ).
fof(f1348,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f508]) ).
fof(f1353,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_field(relation_restriction(X1,X0)),relation_field(X1)) ),
inference(cnf_transformation,[],[f511]) ).
fof(f1359,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| subset(fiber(relation_restriction(X2,X0),X1),fiber(X2,X1)) ),
inference(cnf_transformation,[],[f517]) ).
fof(f1381,plain,
relation(sK108),
inference(cnf_transformation,[],[f826]) ).
fof(f1382,plain,
well_founded_relation(sK108),
inference(cnf_transformation,[],[f826]) ).
fof(f1383,plain,
~ well_founded_relation(relation_restriction(sK108,sK107)),
inference(cnf_transformation,[],[f826]) ).
fof(f1469,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ subset(X0,X1)
| disjoint(X0,X2) ),
inference(cnf_transformation,[],[f597]) ).
tcf(c_172,plain,
! [X0: $i] :
( well_founded_relation(X0)
| subset(sK33(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1002]) ).
tcf(c_173,plain,
! [X0: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ( sK33(X0) != empty_set ) ),
inference(cnf_transformation,[],[f1001]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( well_founded_relation(X0)
| ~ relation(X0)
| ~ in(X1,sK33(X0))
| ~ disjoint(fiber(X0,X1),sK33(X0)) ),
inference(cnf_transformation,[],[f1000]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( in(sK34(X1,X0),X0)
| ( X0 = empty_set )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f999]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(X1,sK34(X1,X0)),X0)
| ( X0 = empty_set )
| ~ well_founded_relation(X1)
| ~ relation(X1)
| ~ subset(X0,relation_field(X1)) ),
inference(cnf_transformation,[],[f998]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1140]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1348]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i] :
( subset(relation_field(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1353]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(fiber(relation_restriction(X0,X1),X2),fiber(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1359]) ).
tcf(c_554,negated_conjecture,
~ well_founded_relation(relation_restriction(sK108,sK107)),
inference(cnf_transformation,[],[f1383]) ).
tcf(c_555,negated_conjecture,
well_founded_relation(sK108),
inference(cnf_transformation,[],[f1382]) ).
tcf(c_556,negated_conjecture,
relation(sK108),
inference(cnf_transformation,[],[f1381]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i,X2: $i] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1469]) ).
tcf(c_24856,definition,
iPr_def_12 = relation_restriction(sK108,sK107),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_24857,negated_conjecture,
relation(sK108),
inference(demodulation,[status(thm)],[c_556]) ).
tcf(c_24858,negated_conjecture,
well_founded_relation(sK108),
inference(demodulation,[status(thm)],[c_555]) ).
tcf(c_24859,negated_conjecture,
~ well_founded_relation(iPr_def_12),
inference(demodulation,[status(thm)],[c_554,c_24856]) ).
tcf(c_35228,plain,
( relation(iPr_def_12)
| ~ relation(sK108) ),
inference(superposition,[status(thm)],[c_24856,c_313]) ).
tcf(c_35229,plain,
relation(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_35228,c_24857]) ).
tcf(c_38215,plain,
( well_founded_relation(iPr_def_12)
| ~ relation(iPr_def_12)
| ( sK33(iPr_def_12) != empty_set ) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_39830,plain,
( subset(relation_field(iPr_def_12),relation_field(sK108))
| ~ relation(sK108) ),
inference(superposition,[status(thm)],[c_24856,c_525]) ).
tcf(c_39832,plain,
subset(relation_field(iPr_def_12),relation_field(sK108)),
inference(forward_subsumption_resolution,[status(thm)],[c_39830,c_24857]) ).
tcf(c_43056,plain,
! [X0: $i] :
( subset(X0,relation_field(sK108))
| ~ subset(X0,relation_field(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_39832,c_521]) ).
tcf(c_44169,plain,
( well_founded_relation(iPr_def_12)
| subset(sK33(iPr_def_12),relation_field(sK108))
| ~ relation(iPr_def_12) ),
inference(superposition,[status(thm)],[c_172,c_43056]) ).
tcf(c_44196,plain,
subset(sK33(iPr_def_12),relation_field(sK108)),
inference(forward_subsumption_resolution,[status(thm)],[c_44169,c_24859,c_35229]) ).
tcf(c_48340,plain,
! [X0: $i] :
( subset(fiber(iPr_def_12,X0),fiber(sK108,X0))
| ~ relation(sK108) ),
inference(superposition,[status(thm)],[c_24856,c_532]) ).
tcf(c_48347,plain,
! [X0: $i] : subset(fiber(iPr_def_12,X0),fiber(sK108,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_48340,c_24857]) ).
tcf(c_48615,plain,
! [X0: $i,X1: $i] :
( disjoint(fiber(iPr_def_12,X0),X1)
| ~ disjoint(fiber(sK108,X0),X1) ),
inference(superposition,[status(thm)],[c_48347,c_641]) ).
tcf(c_131637,plain,
! [X0: $i] :
( disjoint(fiber(iPr_def_12,sK34(sK108,X0)),X0)
| ( X0 = empty_set )
| ~ well_founded_relation(sK108)
| ~ relation(sK108)
| ~ subset(X0,relation_field(sK108)) ),
inference(superposition,[status(thm)],[c_176,c_48615]) ).
tcf(c_131638,plain,
! [X0: $i] :
( disjoint(fiber(iPr_def_12,sK34(sK108,X0)),X0)
| ( X0 = empty_set )
| ~ subset(X0,relation_field(sK108)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_131637,c_24858,c_24857]) ).
tcf(c_132833,plain,
( well_founded_relation(iPr_def_12)
| ( sK33(iPr_def_12) = empty_set )
| ~ relation(iPr_def_12)
| ~ subset(sK33(iPr_def_12),relation_field(sK108))
| ~ in(sK34(sK108,sK33(iPr_def_12)),sK33(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_131638,c_174]) ).
tcf(c_132844,plain,
( ( sK33(iPr_def_12) = empty_set )
| ~ in(sK34(sK108,sK33(iPr_def_12)),sK33(iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_132833,c_24859,c_35229,c_44196]) ).
tcf(c_132905,plain,
~ in(sK34(sK108,sK33(iPr_def_12)),sK33(iPr_def_12)),
inference(global_subsumption_just,[status(thm)],[c_132844,c_24859,c_35229,c_38215,c_132844]) ).
tcf(c_132910,plain,
( ( sK33(iPr_def_12) = empty_set )
| ~ well_founded_relation(sK108)
| ~ relation(sK108)
| ~ subset(sK33(iPr_def_12),relation_field(sK108)) ),
inference(superposition,[status(thm)],[c_175,c_132905]) ).
tcf(c_132911,plain,
sK33(iPr_def_12) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[c_132910,c_24858,c_24857,c_44196]) ).
tcf(c_132977,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_132911,c_38215,c_35229,c_24859]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU256+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/10.38 % Computer : n006.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Thu Sep 24 13:25:40 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.41 Running first-order theorem proving
% 0.14/10.41 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
% 0.14/10.43
% 0.14/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.43
% 0.14/10.43 % Detected problem language: tptp
% 0.14/10.44 % Proving...
% 65.26/19.95 % SZS status Started for theBenchmark.p
% 65.26/19.95 % SZS status Theorem for theBenchmark.p
% 65.26/19.95
% 65.26/19.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 65.26/19.95
% 65.26/19.95 % ------ iProver source info
% 65.26/19.95
% 65.26/19.95 % git: date: 2026-07-19 20:42:38 +0200
% 65.26/19.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 65.26/19.95 % git: non_committed_changes: false
% 65.26/19.95
% 65.26/19.95 % ------ Parsing...
% 65.26/19.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 65.26/19.95
% 65.26/19.95 % ------ Preprocessing... sup_sim: 57 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 65.26/19.95
% 65.26/19.95 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 65.26/19.95
% 65.26/19.95 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 65.26/19.95 % ------ Proving...
% 65.26/19.95 % ------ Problem Properties
% 65.26/19.95
% 65.26/19.95 %
% 65.26/19.95 % clauses 560
% 65.26/19.95 % conjectures 3
% 65.26/19.95 % EPR 86
% 65.26/19.95 % Horn 432
% 65.26/19.95 % unary 84
% 65.26/19.95 % binary 148
% 65.26/19.95 % lits 1620
% 65.26/19.95 % lits eq 264
% 65.26/19.95 % fd_pure 0
% 65.26/19.95 % fd_pseudo 0
% 65.26/19.95 % fd_cond 21
% 65.26/19.95 % fd_pseudo_cond 99
% 65.26/19.95 % AC symbols 0
% 65.26/19.95
% 65.26/19.95 % ------ Schedule dynamic 5 is on
% 65.26/19.95
% 65.26/19.95 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 65.26/19.95
% 65.26/19.95
% 65.26/19.95 % ------
% 65.26/19.95 % Current options:
% 65.26/19.95 % ------
% 65.26/19.95
% 65.26/19.95
% 65.26/19.95 %
% 65.26/19.95
% 65.26/19.95 % ------ Proving...
% 65.26/19.95 %
% 65.26/19.95
% 65.26/19.95 % SZS status Theorem for theBenchmark.p
% 65.26/19.95
% 65.26/19.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 65.26/19.95
% 65.26/19.95
%------------------------------------------------------------------------------