%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU361+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 : n009.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 02:57:13 PM UTC 2026
% Result : Theorem 6.77s 1.79s
% Output : CNFRefutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 15 unt; 0 def)
% Number of atoms : 225 ( 17 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 289 ( 118 ~; 106 |; 48 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 0 sgn 73 !; 7 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [X0] :
( rel_str(X0)
=> bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(f161,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( ex_sup_of_relstr_set(X0,X1)
=> ( X2 = join_on_relstr(X0,X1)
<=> ( ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& relstr_set_smaller(X0,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_yellow_0) ).
fof(f185,axiom,
! [X0,X1] :
( rel_str(X0)
=> element(join_on_relstr(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
fof(f605,axiom,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0) )
=> ( ex_inf_of_relstr_set(X0,the_carrier(X0))
& ex_sup_of_relstr_set(X0,empty_set) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(f610,conjecture,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> related(X0,bottom_of_relstr(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(f611,negated_conjecture,
~ ! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> related(X0,bottom_of_relstr(X0),X1) ) ),
inference(negated_conjecture,[status(cth)],[f610]) ).
fof(f660,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f825,plain,
! [X0] :
( ~ rel_str(X0)
| bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
inference(ennf_transformation,[],[f56]) ).
fof(f950,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ( X2 = join_on_relstr(X0,X1)
<=> ( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3) )
& relstr_set_smaller(X0,X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f161]) ).
fof(f951,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ( X2 = join_on_relstr(X0,X1)
<=> ( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3) )
& relstr_set_smaller(X0,X1,X2) ) ) ) ),
inference(flattening,[],[f950]) ).
fof(f968,plain,
! [X0,X1] :
( ~ rel_str(X0)
| element(join_on_relstr(X0,X1),the_carrier(X0)) ),
inference(ennf_transformation,[],[f185]) ).
fof(f1451,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0)
| ( ex_inf_of_relstr_set(X0,the_carrier(X0))
& ex_sup_of_relstr_set(X0,empty_set) ) ),
inference(ennf_transformation,[],[f605]) ).
fof(f1452,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0)
| ( ex_inf_of_relstr_set(X0,the_carrier(X0))
& ex_sup_of_relstr_set(X0,empty_set) ) ),
inference(flattening,[],[f1451]) ).
fof(f1458,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ~ related(X0,bottom_of_relstr(X0),X1) ) ),
inference(ennf_transformation,[],[f611]) ).
fof(f1459,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ~ related(X0,bottom_of_relstr(X0),X1) ) ),
inference(flattening,[],[f1458]) ).
fof(f1529,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
inference(ennf_transformation,[],[f660]) ).
fof(f1903,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ( ( join_on_relstr(X0,X1) != X2
| ( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3) )
& relstr_set_smaller(X0,X1,X2) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& relstr_set_smaller(X0,X1,X3)
& ~ related(X0,X2,X3) )
| ~ relstr_set_smaller(X0,X1,X2)
| X2 = join_on_relstr(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f951]) ).
fof(f1904,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ( ( join_on_relstr(X0,X1) != X2
| ( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3) )
& relstr_set_smaller(X0,X1,X2) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& relstr_set_smaller(X0,X1,X3)
& ~ related(X0,X2,X3) )
| ~ relstr_set_smaller(X0,X1,X2)
| X2 = join_on_relstr(X0,X1) ) ) ) ),
inference(flattening,[],[f1903]) ).
fof(f1905,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ( ( join_on_relstr(X0,X1) != X2
| ( ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X4)
| related(X0,X2,X4) )
& relstr_set_smaller(X0,X1,X2) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& relstr_set_smaller(X0,X1,X3)
& ~ related(X0,X2,X3) )
| ~ relstr_set_smaller(X0,X1,X2)
| X2 = join_on_relstr(X0,X1) ) ) ) ),
inference(rectify,[],[f1904]) ).
fof(f1906,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ( ( join_on_relstr(X0,X1) != X2
| ( ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X4)
| related(X0,X2,X4) )
& relstr_set_smaller(X0,X1,X2) ) )
& ( ( element(sK180(X0,X1,X2),the_carrier(X0))
& relstr_set_smaller(X0,X1,sK180(X0,X1,X2))
& ~ related(X0,X2,sK180(X0,X1,X2)) )
| ~ relstr_set_smaller(X0,X1,X2)
| X2 = join_on_relstr(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(X3,sK180(X0,X1,X2))],[f1905]) ).
fof(f2305,plain,
( rel_str(sK509)
& lower_bounded_relstr(sK509)
& antisymmetric_relstr(sK509)
& ~ empty_carrier(sK509)
& element(sK510,the_carrier(sK509))
& ~ related(sK509,bottom_of_relstr(sK509),sK510) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK509,sK510]),skolemize(X0,sK509),skolemize(X1,sK510)],[f1459]) ).
fof(f2460,plain,
! [X0] :
( ~ rel_str(X0)
| bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
inference(cnf_transformation,[],[f825]) ).
fof(f2897,plain,
! [X2,X0,X1,X4] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| join_on_relstr(X0,X1) != X2
| ~ element(X4,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X4)
| related(X0,X2,X4) ),
inference(cnf_transformation,[],[f1906]) ).
fof(f2917,plain,
! [X0,X1] :
( ~ rel_str(X0)
| element(join_on_relstr(X0,X1),the_carrier(X0)) ),
inference(cnf_transformation,[],[f968]) ).
fof(f4121,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0)
| ex_sup_of_relstr_set(X0,empty_set) ),
inference(cnf_transformation,[],[f1452]) ).
fof(f4129,plain,
rel_str(sK509),
inference(cnf_transformation,[],[f2305]) ).
fof(f4130,plain,
lower_bounded_relstr(sK509),
inference(cnf_transformation,[],[f2305]) ).
fof(f4131,plain,
antisymmetric_relstr(sK509),
inference(cnf_transformation,[],[f2305]) ).
fof(f4132,plain,
~ empty_carrier(sK509),
inference(cnf_transformation,[],[f2305]) ).
fof(f4133,plain,
element(sK510,the_carrier(sK509)),
inference(cnf_transformation,[],[f2305]) ).
fof(f4134,plain,
~ related(sK509,bottom_of_relstr(sK509),sK510),
inference(cnf_transformation,[],[f2305]) ).
fof(f4222,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| relstr_set_smaller(X0,empty_set,X1) ),
inference(cnf_transformation,[],[f1529]) ).
fof(f5101,plain,
! [X0,X1,X4] :
( ~ rel_str(X0)
| ~ element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X4,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X4)
| related(X0,join_on_relstr(X0,X1),X4) ),
inference(equality_resolution,[],[f2897]) ).
tcf(c_150,plain,
! [X0: $i] :
( ( join_on_relstr(X0,empty_set) = bottom_of_relstr(X0) )
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f2460]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i,X2: $i] :
( related(X0,join_on_relstr(X0,X1),X2)
| ~ rel_str(X0)
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(join_on_relstr(X0,X1),the_carrier(X0)) ),
inference(cnf_transformation,[],[f5101]) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] :
( element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f2917]) ).
tcf(c_1806,plain,
! [X0: $i] :
( empty_carrier(X0)
| ex_sup_of_relstr_set(X0,empty_set)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f4121]) ).
tcf(c_1815,negated_conjecture,
~ related(sK509,bottom_of_relstr(sK509),sK510),
inference(cnf_transformation,[],[f4134]) ).
tcf(c_1816,negated_conjecture,
element(sK510,the_carrier(sK509)),
inference(cnf_transformation,[],[f4133]) ).
tcf(c_1817,negated_conjecture,
~ empty_carrier(sK509),
inference(cnf_transformation,[],[f4132]) ).
tcf(c_1818,negated_conjecture,
antisymmetric_relstr(sK509),
inference(cnf_transformation,[],[f4131]) ).
tcf(c_1819,negated_conjecture,
lower_bounded_relstr(sK509),
inference(cnf_transformation,[],[f4130]) ).
tcf(c_1820,negated_conjecture,
rel_str(sK509),
inference(cnf_transformation,[],[f4129]) ).
tcf(c_1905,plain,
! [X0: $i,X1: $i] :
( relstr_set_smaller(X1,empty_set,X0)
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f4222]) ).
tcf(c_2506,plain,
join_on_relstr(sK509,empty_set) = bottom_of_relstr(sK509),
inference(superposition,[status(thm)],[c_1820,c_150]) ).
tcf(c_2529,plain,
( relstr_set_smaller(sK509,empty_set,sK510)
| ~ rel_str(sK509) ),
inference(superposition,[status(thm)],[c_1816,c_1905]) ).
tcf(c_2629,plain,
! [X0: $i,X1: $i,X2: $i] :
( related(X0,join_on_relstr(X0,X1),X2)
| ~ rel_str(X0)
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_589,c_605,c_589]) ).
tcf(c_2644,plain,
! [X0: $i] :
( related(sK509,bottom_of_relstr(sK509),X0)
| ~ rel_str(sK509)
| ~ ex_sup_of_relstr_set(sK509,empty_set)
| ~ relstr_set_smaller(sK509,empty_set,X0)
| ~ element(X0,the_carrier(sK509)) ),
inference(superposition,[status(thm)],[c_2506,c_2629]) ).
tcf(c_3013,plain,
! [X0: $i] :
( related(sK509,bottom_of_relstr(sK509),X0)
| ~ element(X0,the_carrier(sK509))
| ~ relstr_set_smaller(sK509,empty_set,X0)
| ~ ex_sup_of_relstr_set(sK509,empty_set) ),
inference(global_subsumption_just,[status(thm)],[c_2644,c_1820,c_2644]) ).
tcf(c_3014,plain,
! [X0: $i] :
( related(sK509,bottom_of_relstr(sK509),X0)
| ~ ex_sup_of_relstr_set(sK509,empty_set)
| ~ relstr_set_smaller(sK509,empty_set,X0)
| ~ element(X0,the_carrier(sK509)) ),
inference(renaming,[status(thm)],[c_3013]) ).
tcf(c_3024,plain,
( ~ ex_sup_of_relstr_set(sK509,empty_set)
| ~ relstr_set_smaller(sK509,empty_set,sK510)
| ~ element(sK510,the_carrier(sK509)) ),
inference(superposition,[status(thm)],[c_3014,c_1815]) ).
tcf(c_3505,plain,
~ ex_sup_of_relstr_set(sK509,empty_set),
inference(global_subsumption_just,[status(thm)],[c_3024,c_1820,c_1816,c_2529,c_3024]) ).
tcf(c_3507,plain,
( empty_carrier(sK509)
| ~ antisymmetric_relstr(sK509)
| ~ lower_bounded_relstr(sK509)
| ~ rel_str(sK509) ),
inference(superposition,[status(thm)],[c_1806,c_3505]) ).
tcf(c_3508,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3507,c_1817,c_1818,c_1819,c_1820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU361+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 % Computer : n009.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Thu Sep 24 13:50:44 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.45 Running first-order theorem proving
% 0.10/0.45 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
% 0.15/0.47
% 0.15/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.47
% 0.15/0.47 % Detected problem language: tptp
% 0.15/0.48 % Proving...
% 6.77/1.79 % SZS status Started for theBenchmark.p
% 6.77/1.79 % SZS status Theorem for theBenchmark.p
% 6.77/1.79
% 6.77/1.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.77/1.79
% 6.77/1.79 % ------ iProver source info
% 6.77/1.79
% 6.77/1.79 % git: date: 2026-07-19 20:42:38 +0200
% 6.77/1.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.77/1.79 % git: non_committed_changes: false
% 6.77/1.79
% 6.77/1.79 % ------ Parsing...
% 6.77/1.79 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 6.77/1.79 % ------ Proving...
% 6.77/1.79 % ------ Problem Properties
% 6.77/1.79
% 6.77/1.79 %
% 6.77/1.79 % clauses 1905
% 6.77/1.79 % conjectures 6
% 6.77/1.79 % EPR 277
% 6.77/1.79 % Horn 1354
% 6.77/1.79 % unary 251
% 6.77/1.79 % binary 493
% 6.77/1.79 % lits 6248
% 6.77/1.79 % lits eq 691
% 6.77/1.79 % fd_pure 0
% 6.77/1.79 % fd_pseudo 0
% 6.77/1.79 % fd_cond 53
% 6.77/1.79 % fd_pseudo_cond 149
% 6.77/1.79 % AC symbols 0
% 6.77/1.79
% 6.77/1.79 % ------ Input Options Time Limit: Unbounded
% 6.77/1.79
% 6.77/1.79
% 6.77/1.79 % ------
% 6.77/1.79 % Current options:
% 6.77/1.79 % ------
% 6.77/1.79
% 6.77/1.79
% 6.77/1.79 %
% 6.77/1.79
% 6.77/1.79 % ------ Proving...
% 6.77/1.79 %
% 6.77/1.79
% 6.77/1.79 % ------ Proving...
% 6.77/1.79 %
% 6.77/1.79
% 6.77/1.79 % SZS status Theorem for theBenchmark.p
% 6.77/1.79
% 6.77/1.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.77/1.79
% 6.77/1.79
%------------------------------------------------------------------------------