%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU383+1 : 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 : n010.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 02:57:17 PM UTC 2026
% Result : Theorem 7.39s 1.74s
% Output : CNFRefutation 7.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 139 ( 31 unt; 0 def)
% Number of atoms : 540 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 666 ( 265 ~; 255 |; 113 &)
% ( 9 <=>; 21 =>; 0 <=; 3 <~>)
% Maximal formula depth : 16 ( 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 : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 197 ( 0 sgn 178 !; 19 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( upper_relstr_subset(X1,X0)
<=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( ( related(X0,X2,X3)
& in(X2,X1) )
=> in(X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_waybel_0) ).
fof(f12,axiom,
! [X0] :
( rel_str(X0)
=> element(bottom_of_relstr(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f23,axiom,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_waybel_0) ).
fof(f34,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f36,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f38,axiom,
! [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(f39,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f41,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f45,conjecture,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1) )
=> ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_7) ).
fof(f46,negated_conjecture,
~ ! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1) )
=> ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f23]) ).
fof(f48,plain,
~ ! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& ~ empty(X1) )
=> ( proper_element(X1,powerset(the_carrier(X0)))
<=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
inference(pure_predicate_removal,[],[f46]) ).
fof(f49,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& ~ empty(X1)
& ( proper_element(X1,powerset(the_carrier(X0)))
<~> ~ in(bottom_of_relstr(X0),X1) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f50,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& ~ empty(X1)
& ( proper_element(X1,powerset(the_carrier(X0)))
<~> ~ in(bottom_of_relstr(X0),X1) ) ) ),
inference(flattening,[],[f49]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f60,plain,
! [X0] :
( ~ rel_str(X0)
| element(bottom_of_relstr(X0),the_carrier(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f61,plain,
! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ? [X1] :
( upper_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f62,plain,
! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ? [X1] :
( upper_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(flattening,[],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( upper_relstr_subset(X1,X0)
<=> ! [X2] :
( ~ element(X2,the_carrier(X0))
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ related(X0,X2,X3)
| ~ in(X2,X1)
| in(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f66,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( upper_relstr_subset(X1,X0)
<=> ! [X2] :
( ~ element(X2,the_carrier(X0))
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ related(X0,X2,X3)
| ~ in(X2,X1)
| in(X3,X1) ) ) ) ) ),
inference(flattening,[],[f65]) ).
fof(f67,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,[],[f38]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f36]) ).
fof(f76,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& ~ empty(X1)
& ( proper_element(X1,powerset(the_carrier(X0)))
| ~ in(bottom_of_relstr(X0),X1) )
& ( ~ proper_element(X1,powerset(the_carrier(X0)))
| in(bottom_of_relstr(X0),X1) ) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f77,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& upper_relstr_subset(X1,X0)
& ~ empty(X1)
& ( proper_element(X1,powerset(the_carrier(X0)))
| ~ in(bottom_of_relstr(X0),X1) )
& ( ~ proper_element(X1,powerset(the_carrier(X0)))
| in(bottom_of_relstr(X0),X1) ) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( rel_str(sK0)
& lower_bounded_relstr(sK0)
& antisymmetric_relstr(sK0)
& transitive_relstr(sK0)
& reflexive_relstr(sK0)
& ~ empty_carrier(sK0)
& element(sK1,powerset(the_carrier(sK0)))
& upper_relstr_subset(sK1,sK0)
& ~ empty(sK1)
& ( proper_element(sK1,powerset(the_carrier(sK0)))
| ~ in(bottom_of_relstr(sK0),sK1) )
& ( ~ proper_element(sK1,powerset(the_carrier(sK0)))
| in(bottom_of_relstr(sK0),sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f77]) ).
fof(f84,plain,
! [X0] : element(sK7(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f19]) ).
fof(f85,plain,
! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ( upper_relstr_subset(sK8(X0),X0)
& ~ empty(sK8(X0))
& element(sK8(X0),powerset(the_carrier(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f62]) ).
fof(f86,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ upper_relstr_subset(X1,X0)
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ related(X0,X2,X3)
| ~ in(X2,X1)
| in(X3,X1) ) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X2,X3)
& in(X2,X1)
& ~ in(X3,X1) ) )
| upper_relstr_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f87,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ upper_relstr_subset(X1,X0)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ! [X5] :
( ~ element(X5,the_carrier(X0))
| ~ related(X0,X4,X5)
| ~ in(X4,X1)
| in(X5,X1) ) ) )
& ( ? [X2] :
( element(X2,the_carrier(X0))
& ? [X3] :
( element(X3,the_carrier(X0))
& related(X0,X2,X3)
& in(X2,X1)
& ~ in(X3,X1) ) )
| upper_relstr_subset(X1,X0) ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ upper_relstr_subset(X1,X0)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ! [X5] :
( ~ element(X5,the_carrier(X0))
| ~ related(X0,X4,X5)
| ~ in(X4,X1)
| in(X5,X1) ) ) )
& ( ( element(sK9(X0,X1),the_carrier(X0))
& element(sK10(X0,X1),the_carrier(X0))
& related(X0,sK9(X0,X1),sK10(X0,X1))
& in(sK9(X0,X1),X1)
& ~ in(sK10(X0,X1),X1) )
| upper_relstr_subset(X1,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X2,sK9(X0,X1)),skolemize(X3,sK10(X0,X1))],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ( ( ~ proper_element(X1,powerset(X0))
| X1 != X0 )
& ( X0 = X1
| proper_element(X1,powerset(X0)) ) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f75]) ).
fof(f91,plain,
! [X0,X1] :
( ( ( in(sK11(X0,X1),X0)
| in(sK11(X0,X1),X1) )
& ( ~ in(sK11(X0,X1),X0)
| ~ in(sK11(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f90]) ).
fof(f92,plain,
rel_str(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f93,plain,
lower_bounded_relstr(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f94,plain,
antisymmetric_relstr(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f95,plain,
transitive_relstr(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f96,plain,
reflexive_relstr(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f97,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f98,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f78]) ).
fof(f99,plain,
upper_relstr_subset(sK1,sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f101,plain,
( proper_element(sK1,powerset(the_carrier(sK0)))
| ~ in(bottom_of_relstr(sK0),sK1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f102,plain,
( ~ proper_element(sK1,powerset(the_carrier(sK0)))
| in(bottom_of_relstr(sK0),sK1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f111,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f112,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f114,plain,
! [X0] :
( ~ rel_str(X0)
| element(bottom_of_relstr(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f118,plain,
! [X0] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f84]) ).
fof(f120,plain,
! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ empty(sK8(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f121,plain,
! [X0] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| element(sK8(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f124,plain,
! [X0,X1,X4,X5] :
( ~ rel_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ upper_relstr_subset(X1,X0)
| ~ element(X4,the_carrier(X0))
| ~ element(X5,the_carrier(X0))
| ~ related(X0,X4,X5)
| ~ in(X4,X1)
| in(X5,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f130,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| related(X0,bottom_of_relstr(X0),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f131,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| ~ proper_element(X1,powerset(X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f132,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| X0 = X1
| proper_element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f136,plain,
! [X0,X1] :
( in(sK11(X0,X1),X0)
| in(sK11(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f137,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X0)
| ~ in(sK11(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f138,plain,
! [X1] :
( ~ element(X1,powerset(X1))
| ~ proper_element(X1,powerset(X1)) ),
inference(equality_resolution,[],[f131]) ).
tcf(c_49,negated_conjecture,
( in(bottom_of_relstr(sK0),sK1)
| ~ proper_element(sK1,powerset(the_carrier(sK0))) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_50,negated_conjecture,
( proper_element(sK1,powerset(the_carrier(sK0)))
| ~ in(bottom_of_relstr(sK0),sK1) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_52,negated_conjecture,
upper_relstr_subset(sK1,sK0),
inference(cnf_transformation,[],[f99]) ).
tcf(c_53,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f98]) ).
tcf(c_54,negated_conjecture,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f97]) ).
tcf(c_55,negated_conjecture,
reflexive_relstr(sK0),
inference(cnf_transformation,[],[f96]) ).
tcf(c_56,negated_conjecture,
transitive_relstr(sK0),
inference(cnf_transformation,[],[f95]) ).
tcf(c_57,negated_conjecture,
antisymmetric_relstr(sK0),
inference(cnf_transformation,[],[f94]) ).
tcf(c_58,negated_conjecture,
lower_bounded_relstr(sK0),
inference(cnf_transformation,[],[f93]) ).
tcf(c_59,negated_conjecture,
rel_str(sK0),
inference(cnf_transformation,[],[f92]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_71,plain,
! [X0: $i] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_75,plain,
! [X0: $i] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f118]) ).
tcf(c_76,plain,
! [X0: $i] :
( empty_carrier(X0)
| element(sK8(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_77,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ empty(sK8(X0)) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X0)
| ~ rel_str(X1)
| ~ upper_relstr_subset(X0,X1)
| ~ in(X2,X0)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ related(X1,X2,X3)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X1)
| related(X1,bottom_of_relstr(X1),X0)
| ~ rel_str(X1)
| ~ lower_bounded_relstr(X1)
| ~ antisymmetric_relstr(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( proper_element(X0,powerset(X1))
| ( X0 = X1 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_88,plain,
! [X0: $i] :
( ~ element(X0,powerset(X0))
| ~ proper_element(X0,powerset(X0)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK11(X0,X1),X1)
| ~ in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( in(sK11(X0,X1),X1)
| in(sK11(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_111,plain,
( empty_carrier(sK0)
| ~ rel_str(sK0)
| ~ transitive_relstr(sK0)
| ~ reflexive_relstr(sK0)
| ~ empty(sK8(sK0)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_114,plain,
( empty_carrier(sK0)
| element(sK8(sK0),powerset(the_carrier(sK0)))
| ~ rel_str(sK0)
| ~ transitive_relstr(sK0)
| ~ reflexive_relstr(sK0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_138,plain,
! [X0: $i] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_71]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X3,X0)
| ~ rel_str(X1)
| ~ upper_relstr_subset(X0,X1)
| ~ in(X2,X0)
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X2,X3)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_85,c_67]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i] :
( empty_carrier(X0)
| related(X0,bottom_of_relstr(X0),X1)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ element(X1,the_carrier(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_86]) ).
tcf(c_653,plain,
! [X0: $i] :
( empty_carrier(sK0)
| related(sK0,bottom_of_relstr(sK0),X0)
| ~ rel_str(sK0)
| ~ lower_bounded_relstr(sK0)
| ~ element(X0,the_carrier(sK0)) ),
inference(unflattening,[status(thm)],[c_652]) ).
tcf(c_655,plain,
! [X0: $i] :
( ~ element(X0,the_carrier(sK0))
| related(sK0,bottom_of_relstr(sK0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_653,c_59,c_58,c_54,c_653]) ).
tcf(c_656,plain,
! [X0: $i] :
( related(sK0,bottom_of_relstr(sK0),X0)
| ~ element(X0,the_carrier(sK0)) ),
inference(renaming,[status(thm)],[c_655]) ).
tcf(c_728,plain,
! [X0: $i] :
( ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ empty(sK8(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_77]) ).
tcf(c_729,plain,
( ~ rel_str(sK0)
| ~ transitive_relstr(sK0)
| ~ reflexive_relstr(sK0)
| ~ empty(sK8(sK0)) ),
inference(unflattening,[status(thm)],[c_728]) ).
tcf(c_730,plain,
~ empty(sK8(sK0)),
inference(global_subsumption_just,[status(thm)],[c_729,c_59,c_56,c_55,c_54,c_111]) ).
tcf(c_735,plain,
! [X0: $i] :
( element(sK8(X0),powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_76]) ).
tcf(c_736,plain,
( element(sK8(sK0),powerset(the_carrier(sK0)))
| ~ rel_str(sK0)
| ~ transitive_relstr(sK0)
| ~ reflexive_relstr(sK0) ),
inference(unflattening,[status(thm)],[c_735]) ).
tcf(c_737,plain,
element(sK8(sK0),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_736,c_59,c_56,c_55,c_54,c_114]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(X2,X4)
| ~ rel_str(X0)
| ~ upper_relstr_subset(X4,X0)
| ~ in(X1,X4)
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(X0))
| ~ element(X4,powerset(the_carrier(X0)))
| ( X2 != X3 )
| ( X0 != sK0 )
| ( bottom_of_relstr(sK0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_325,c_656]) ).
tcf(c_772,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ~ rel_str(sK0)
| ~ upper_relstr_subset(X0,sK0)
| ~ element(X1,the_carrier(sK0))
| ~ in(bottom_of_relstr(sK0),X0)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(unflattening,[status(thm)],[c_771]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ in(bottom_of_relstr(sK0),X0)
| ~ element(X1,the_carrier(sK0))
| ~ upper_relstr_subset(X0,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_772,c_59,c_772]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| ~ upper_relstr_subset(X0,sK0)
| ~ element(X1,the_carrier(sK0))
| ~ in(bottom_of_relstr(sK0),X0)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(renaming,[status(thm)],[c_774]) ).
tcf(c_836,plain,
! [X0: $i] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_138]) ).
tcf(c_837,plain,
element(bottom_of_relstr(sK0),the_carrier(sK0)),
inference(unflattening,[status(thm)],[c_836]) ).
tcf(c_2439,plain,
! [X0: $i] :
( empty(X0)
| in(sK7(X0),X0) ),
inference(superposition,[status(thm)],[c_75,c_68]) ).
tcf(c_2440,plain,
( empty(the_carrier(sK0))
| in(bottom_of_relstr(sK0),the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_837,c_68]) ).
tcf(c_2552,plain,
! [X0: $i] :
( in(X0,sK1)
| ~ upper_relstr_subset(sK1,sK0)
| ~ in(bottom_of_relstr(sK0),sK1)
| ~ element(X0,the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_53,c_775]) ).
tcf(c_2557,plain,
! [X0: $i] :
( in(X0,sK1)
| ~ in(bottom_of_relstr(sK0),sK1)
| ~ element(X0,the_carrier(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2552,c_52]) ).
tcf(c_2627,plain,
! [X0: $i] :
( ~ empty(the_carrier(sK0))
| ~ in(X0,sK8(sK0)) ),
inference(superposition,[status(thm)],[c_737,c_66]) ).
tcf(c_2646,plain,
! [X0: $i] :
( element(X0,the_carrier(sK0))
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_53,c_67]) ).
tcf(c_2688,plain,
! [X0: $i] :
( empty(the_carrier(sK0))
| in(X0,the_carrier(sK0))
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_2646,c_68]) ).
tcf(c_2697,plain,
( empty(sK8(sK0))
| ~ empty(the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_2439,c_2627]) ).
tcf(c_2698,plain,
~ empty(the_carrier(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2697,c_730]) ).
tcf(c_2701,plain,
in(bottom_of_relstr(sK0),the_carrier(sK0)),
inference(backward_subsumption_resolution,[status(thm)],[c_2440,c_2698]) ).
tcf(c_2724,plain,
! [X0: $i] :
( ~ in(X0,sK1)
| in(X0,the_carrier(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_2688,c_2688,c_2698]) ).
tcf(c_2725,plain,
! [X0: $i] :
( in(X0,the_carrier(sK0))
| ~ in(X0,sK1) ),
inference(renaming,[status(thm)],[c_2724]) ).
tcf(c_2766,plain,
( proper_element(sK1,powerset(the_carrier(sK0)))
| ( the_carrier(sK0) = sK1 ) ),
inference(superposition,[status(thm)],[c_53,c_87]) ).
tcf(c_2795,plain,
! [X0: $i,X1: $i] :
( element(sK11(X0,X1),X1)
| in(sK11(X0,X1),X0)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_93,c_69]) ).
tcf(c_2843,plain,
! [X0: $i] :
( ( the_carrier(sK0) = X0 )
| ~ in(sK11(X0,the_carrier(sK0)),sK1)
| ~ in(sK11(X0,the_carrier(sK0)),X0) ),
inference(superposition,[status(thm)],[c_2725,c_92]) ).
tcf(c_2888,plain,
( in(bottom_of_relstr(sK0),sK1)
| ( the_carrier(sK0) = sK1 ) ),
inference(superposition,[status(thm)],[c_2766,c_49]) ).
tcf(c_2895,plain,
! [X0: $i] :
( in(X0,sK1)
| ( the_carrier(sK0) = sK1 )
| ~ element(X0,the_carrier(sK0)) ),
inference(superposition,[status(thm)],[c_2888,c_2557]) ).
tcf(c_12338,plain,
! [X0: $i] :
( in(sK11(X0,the_carrier(sK0)),sK1)
| in(sK11(X0,the_carrier(sK0)),X0)
| ( the_carrier(sK0) = sK1 )
| ( the_carrier(sK0) = X0 ) ),
inference(superposition,[status(thm)],[c_2795,c_2895]) ).
tcf(c_14509,plain,
( in(sK11(sK1,the_carrier(sK0)),sK1)
| ( the_carrier(sK0) = sK1 ) ),
inference(equality_factoring,[status(thm)],[c_12338]) ).
tcf(c_14983,plain,
( ( the_carrier(sK0) = sK1 )
| ~ in(sK11(sK1,the_carrier(sK0)),sK1) ),
inference(superposition,[status(thm)],[c_14509,c_2843]) ).
tcf(c_14988,plain,
the_carrier(sK0) = sK1,
inference(backward_subsumption_resolution,[status(thm)],[c_14509,c_14983]) ).
tcf(c_15129,plain,
in(bottom_of_relstr(sK0),sK1),
inference(demodulation,[status(thm)],[c_2701,c_14988]) ).
tcf(c_15151,plain,
( proper_element(sK1,powerset(sK1))
| ~ in(bottom_of_relstr(sK0),sK1) ),
inference(demodulation,[status(thm)],[c_50,c_14988]) ).
tcf(c_15153,plain,
element(sK1,powerset(sK1)),
inference(demodulation,[status(thm)],[c_53,c_14988]) ).
tcf(c_15197,plain,
proper_element(sK1,powerset(sK1)),
inference(backward_subsumption_resolution,[status(thm)],[c_15151,c_15129]) ).
tcf(c_15627,plain,
~ element(sK1,powerset(sK1)),
inference(superposition,[status(thm)],[c_15197,c_88]) ).
tcf(c_15628,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15627,c_15153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU383+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:55:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 7.39/1.74 % SZS status Started for theBenchmark.p
% 7.39/1.74 % SZS status Theorem for theBenchmark.p
% 7.39/1.74
% 7.39/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.39/1.74
% 7.39/1.74 % ------ iProver source info
% 7.39/1.74
% 7.39/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 7.39/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.39/1.74 % git: non_committed_changes: false
% 7.39/1.74
% 7.39/1.74 % ------ Parsing...
% 7.39/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.39/1.74
% 7.39/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 7.39/1.74
% 7.39/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.39/1.74
% 7.39/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.39/1.74 % ------ Proving...
% 7.39/1.74 % ------ Problem Properties
% 7.39/1.74
% 7.39/1.74 %
% 7.39/1.74 % clauses 40
% 7.39/1.74 % conjectures 5
% 7.39/1.74 % EPR 9
% 7.39/1.74 % Horn 28
% 7.39/1.74 % unary 14
% 7.39/1.74 % binary 8
% 7.39/1.74 % lits 92
% 7.39/1.74 % lits eq 4
% 7.39/1.74 % fd_pure 0
% 7.39/1.74 % fd_pseudo 0
% 7.39/1.74 % fd_cond 0
% 7.39/1.74 % fd_pseudo_cond 4
% 7.39/1.74 % AC symbols 0
% 7.39/1.74
% 7.39/1.74 % ------ Schedule dynamic 5 is on
% 7.39/1.74
% 7.39/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.39/1.74
% 7.39/1.74
% 7.39/1.74 % ------
% 7.39/1.74 % Current options:
% 7.39/1.74 % ------
% 7.39/1.74
% 7.39/1.74
% 7.39/1.74 %
% 7.39/1.74
% 7.39/1.74 % ------ Proving...
% 7.39/1.74 %
% 7.39/1.74
% 7.39/1.74 % SZS status Theorem for theBenchmark.p
% 7.39/1.74
% 7.39/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.39/1.74
% 7.39/1.74
%------------------------------------------------------------------------------