%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU310+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 02:56:35 PM UTC 2026
% Result : Theorem 2.28s 1.28s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 4
% Syntax : Number of formulae : 99 ( 16 unt; 2 def)
% Number of atoms : 471 ( 71 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 520 ( 186 ~; 235 |; 82 &)
% ( 7 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 190 ( 0 sgn 147 !; 43 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f37,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X4 = X3
& in(X4,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
fof(f38,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3 )
=> X3 = X4 )
=> ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ) ),
inference(rectify,[],[f37]) ).
fof(f56,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f57,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f56]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 )
| ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 )
| ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f79]) ).
fof(f83,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
? [X3] :
( ( in(X3,X2)
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& ( ~ in(X3,X2)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0))) ) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f84,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
? [X3] :
( ( in(X3,X2)
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& ( ~ in(X3,X2)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0))) ) ) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
( element(sK2,powerset(powerset(the_carrier(sK1))))
& top_str(sK1)
& topological_space(sK1)
& ! [X2] :
( ( in(sK3(X2),X2)
| ( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
& in(sK3(X2),powerset(the_carrier(sK1))) ) )
& ( ~ in(sK3(X2),X2)
| ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| ~ in(sK3(X2),powerset(the_carrier(sK1))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X3,sK3(X2))],[f84]) ).
fof(f93,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ? [X5] :
! [X6] :
( ( ~ in(X6,X5)
| ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) )
& ( ! [X7] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X6),X1)
| X6 != X7
| ~ in(X7,powerset(the_carrier(X0))) )
| in(X6,X5) ) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f94,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X5] :
( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X3 = X5
& in(X5,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ! [X3] :
( ( ~ in(X3,sK11(X0,X1))
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& sK12(X0,X1,X3) = X3
& in(sK12(X0,X1,X3),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0))) )
| in(X3,sK11(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X2,sK11(X0,X1)),skolemize(X5,sK12(X0,X1,X3))],[f94]) ).
fof(f96,plain,
element(sK2,powerset(powerset(the_carrier(sK1)))),
inference(cnf_transformation,[],[f85]) ).
fof(f97,plain,
top_str(sK1),
inference(cnf_transformation,[],[f85]) ).
fof(f98,plain,
topological_space(sK1),
inference(cnf_transformation,[],[f85]) ).
fof(f99,plain,
! [X2] :
( in(sK3(X2),X2)
| in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f100,plain,
! [X2] :
( in(sK3(X2),X2)
| in(sK3(X2),powerset(the_carrier(sK1))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f101,plain,
! [X2] :
( ~ in(sK3(X2),X2)
| ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
| ~ in(sK3(X2),powerset(the_carrier(sK1))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f161,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ~ in(X3,sK11(X0,X1))
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ~ in(X3,sK11(X0,X1))
| sK12(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f95]) ).
fof(f163,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ~ in(X3,sK11(X0,X1))
| in(sK12(X0,X1,X3),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f164,plain,
! [X3,X0,X1,X4] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| X3 != X4
| ~ in(X4,powerset(the_carrier(X0)))
| in(X3,sK11(X0,X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f165,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ~ in(set_difference(cast_as_carrier_subset(X0),X4),X1)
| ~ in(X4,powerset(the_carrier(X0)))
| in(X4,sK11(X0,X1)) ),
inference(equality_resolution,[],[f164]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ in(sK3(X0),X0)
| ~ in(sK3(X0),powerset(the_carrier(sK1)))
| ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X0)),sK2) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(sK3(X0),X0)
| in(sK3(X0),powerset(the_carrier(sK1))) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(sK3(X0),X0)
| in(set_difference(cast_as_carrier_subset(sK1),sK3(X0)),sK2) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_52,negated_conjecture,
topological_space(sK1),
inference(cnf_transformation,[],[f98]) ).
tcf(c_53,negated_conjecture,
top_str(sK1),
inference(cnf_transformation,[],[f97]) ).
tcf(c_54,negated_conjecture,
element(sK2,powerset(powerset(the_carrier(sK1)))),
inference(cnf_transformation,[],[f96]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X0)
| in(X1,sK11(X0,X2))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1)
| in(sK12(X1,X0,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK11(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1)
| ( sK12(X1,X0,X2) = X2 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK11(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1)
| in(set_difference(cast_as_carrier_subset(X1),X2),X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK11(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_811,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X0)
| in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ top_str(X0)
| ~ in(X2,sK11(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_117]) ).
tcf(c_812,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
| ~ top_str(sK1)
| ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1)))) ),
inference(unflattening,[status(thm)],[c_811]) ).
tcf(c_814,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_812,c_53,c_812]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
| ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1)))) ),
inference(renaming,[status(thm)],[c_814]) ).
tcf(c_829,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X0)
| ( sK12(X0,X1,X2) = X2 )
| ~ top_str(X0)
| ~ in(X2,sK11(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_116]) ).
tcf(c_830,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| ( sK12(sK1,X0,X1) = X1 )
| ~ top_str(sK1)
| ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1)))) ),
inference(unflattening,[status(thm)],[c_829]) ).
tcf(c_832,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| ( sK12(sK1,X0,X1) = X1 )
| ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_830,c_53,c_830]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| ( sK12(sK1,X0,X1) = X1 )
| ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1)))) ),
inference(renaming,[status(thm)],[c_832]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X0)
| in(sK12(X0,X1,X2),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ in(X2,sK11(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_115]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
| ~ top_str(sK1)
| ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1)))) ),
inference(unflattening,[status(thm)],[c_847]) ).
tcf(c_850,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
| ~ element(X0,powerset(powerset(the_carrier(sK1))))
| ~ in(X1,sK11(sK1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_848,c_53,c_848]) ).
tcf(c_851,plain,
! [X0: $i,X1: $i] :
( sP0(X0,sK1)
| in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
| ~ in(X1,sK11(sK1,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK1)))) ),
inference(renaming,[status(thm)],[c_850]) ).
tcf(c_865,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2,X0)
| in(X1,sK11(X0,X2))
| ~ top_str(X0)
| ~ in(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(powerset(the_carrier(X0))))
| ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_114]) ).
tcf(c_866,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK1)
| in(X0,sK11(sK1,X1))
| ~ top_str(sK1)
| ~ in(X0,powerset(the_carrier(sK1)))
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1) ),
inference(unflattening,[status(thm)],[c_865]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK1)
| in(X0,sK11(sK1,X1))
| ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1)
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| ~ in(X0,powerset(the_carrier(sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_866,c_53,c_866]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK1)
| in(X0,sK11(sK1,X1))
| ~ in(X0,powerset(the_carrier(sK1)))
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1) ),
inference(renaming,[status(thm)],[c_868]) ).
tcf(c_2667,definition,
iPr_def_14 = powerset(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2670,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK1)
| in(X0,sK11(sK1,X1))
| ~ element(X1,iPr_def_14)
| ~ in(X0,iPr_def_12)
| ~ in(set_difference(iPr_def_10,X0),X1) ),
inference(demodulation,[status(thm)],[c_869,c_2667]) ).
tcf(c_2671,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK1)
| in(sK12(sK1,X1,X0),iPr_def_12)
| ~ element(X1,iPr_def_14)
| ~ in(X0,sK11(sK1,X1)) ),
inference(demodulation,[status(thm)],[c_851]) ).
tcf(c_2672,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK1)
| ( sK12(sK1,X1,X0) = X0 )
| ~ element(X1,iPr_def_14)
| ~ in(X0,sK11(sK1,X1)) ),
inference(demodulation,[status(thm)],[c_833]) ).
tcf(c_2673,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK1)
| in(set_difference(iPr_def_10,X0),X1)
| ~ element(X1,iPr_def_14)
| ~ in(X0,sK11(sK1,X1)) ),
inference(demodulation,[status(thm)],[c_815]) ).
tcf(c_2674,negated_conjecture,
element(sK2,iPr_def_14),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_2675,negated_conjecture,
! [X0: $i] :
( in(sK3(X0),X0)
| in(set_difference(iPr_def_10,sK3(X0)),sK2) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_2676,negated_conjecture,
! [X0: $i] :
( in(sK3(X0),iPr_def_12)
| in(sK3(X0),X0) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_2677,negated_conjecture,
! [X0: $i] :
( ~ in(sK3(X0),iPr_def_12)
| ~ in(sK3(X0),X0)
| ~ in(set_difference(iPr_def_10,sK3(X0)),sK2) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_3073,plain,
! [X0: $i] :
( sP0(X0,sK1)
| in(set_difference(iPr_def_10,sK3(sK11(sK1,X0))),sK2)
| in(set_difference(iPr_def_10,sK3(sK11(sK1,X0))),X0)
| ~ element(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_2675,c_2673]) ).
tcf(c_3115,plain,
( sP0(sK2,sK1)
| in(set_difference(iPr_def_10,sK3(sK11(sK1,sK2))),sK2)
| ~ element(sK2,iPr_def_14) ),
inference(equality_factoring,[status(thm)],[c_3073]) ).
tcf(c_3117,plain,
( sP0(sK2,sK1)
| in(set_difference(iPr_def_10,sK3(sK11(sK1,sK2))),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3115,c_2674]) ).
tcf(c_3137,plain,
( sP0(sK2,sK1)
| ~ in(sK3(sK11(sK1,sK2)),iPr_def_12)
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_3117,c_2677]) ).
tcf(c_3169,plain,
! [X0: $i] :
( sP0(X0,sK1)
| in(sK3(sK11(sK1,X0)),iPr_def_12)
| ( sK12(sK1,X0,sK3(sK11(sK1,X0))) = sK3(sK11(sK1,X0)) )
| ~ element(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_2676,c_2672]) ).
tcf(c_3332,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ element(sK2,iPr_def_14)
| ~ in(sK3(sK11(sK1,sK2)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_3117,c_2670]) ).
tcf(c_3333,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
| ~ in(sK3(sK11(sK1,sK2)),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3332,c_2674]) ).
tcf(c_3488,plain,
( sP0(sK2,sK1)
| ~ in(sK3(sK11(sK1,sK2)),iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_3333,c_3137,c_3333]) ).
tcf(c_3494,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_2676,c_3488]) ).
tcf(c_3495,plain,
( sP0(sK2,sK1)
| ( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)) )
| ~ element(sK2,iPr_def_14) ),
inference(superposition,[status(thm)],[c_3169,c_3488]) ).
tcf(c_3498,plain,
( sP0(sK2,sK1)
| ( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3495,c_2674]) ).
fof(f81,definition,
! [X1,X0] :
( ~ sP0(X1,X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f82,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP0(X1,X0)
| ? [X5] :
! [X6] :
( in(X6,X5)
<=> ? [X7] :
( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
& X6 = X7
& in(X7,powerset(the_carrier(X0))) ) ) ),
inference(definition_folding,[],[f80,f81]) ).
fof(f90,plain,
! [X1,X0] :
( ~ sP0(X1,X0)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f91,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2,X3,X4] :
( in(set_difference(cast_as_carrier_subset(X1),X4),X0)
& X2 = X4
& in(set_difference(cast_as_carrier_subset(X1),X3),X0)
& X2 = X3
& X3 != X4 ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( in(set_difference(cast_as_carrier_subset(X1),sK10(X0,X1)),X0)
& sK8(X0,X1) = sK10(X0,X1)
& in(set_difference(cast_as_carrier_subset(X1),sK9(X0,X1)),X0)
& sK8(X0,X1) = sK9(X0,X1)
& sK9(X0,X1) != sK10(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1))],[f91]) ).
fof(f157,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK8(X0,X1) = sK10(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f159,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK8(X0,X1) = sK9(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f160,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK9(X0,X1) != sK10(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0,X1)
| ( sK9(X0,X1) != sK10(X0,X1) ) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ( sK9(X0,X1) = sK8(X0,X1) )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( sK10(X0,X1) = sK8(X0,X1) )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_3526,plain,
( ( sK10(sK2,sK1) = sK8(sK2,sK1) )
| ( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_3498,c_112]) ).
tcf(c_3527,plain,
( ( sK9(sK2,sK1) = sK8(sK2,sK1) )
| ( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_3498,c_110]) ).
tcf(c_3610,plain,
( ( sK10(sK2,sK1) = sK8(sK2,sK1) )
| ~ sP0(sK2,sK1) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_3611,plain,
( ( sK9(sK2,sK1) = sK8(sK2,sK1) )
| ~ sP0(sK2,sK1) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_3628,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),iPr_def_12)
| ( sK10(sK2,sK1) = sK8(sK2,sK1) )
| ~ element(sK2,iPr_def_14)
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_3526,c_2671]) ).
tcf(c_3629,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),iPr_def_12)
| ( sK10(sK2,sK1) = sK8(sK2,sK1) )
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3628,c_2674]) ).
tcf(c_3685,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),iPr_def_12)
| ( sK9(sK2,sK1) = sK8(sK2,sK1) )
| ~ element(sK2,iPr_def_14)
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_3527,c_2671]) ).
tcf(c_3686,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),iPr_def_12)
| ( sK9(sK2,sK1) = sK8(sK2,sK1) )
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3685,c_2674]) ).
tcf(c_3696,plain,
sK10(sK2,sK1) = sK8(sK2,sK1),
inference(global_subsumption_just,[status(thm)],[c_3629,c_3488,c_3494,c_3610,c_3629]) ).
tcf(c_3702,plain,
sK9(sK2,sK1) = sK8(sK2,sK1),
inference(global_subsumption_just,[status(thm)],[c_3686,c_3488,c_3494,c_3611,c_3686]) ).
tcf(c_3704,plain,
sK9(sK2,sK1) = sK10(sK2,sK1),
inference(demodulation,[status(thm)],[c_3696,c_3702]) ).
tcf(c_3710,plain,
~ sP0(sK2,sK1),
inference(superposition,[status(thm)],[c_3704,c_109]) ).
tcf(c_3720,plain,
sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_3498,c_3710]) ).
tcf(c_3721,plain,
in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_3494,c_3710]) ).
tcf(c_3722,plain,
~ in(sK3(sK11(sK1,sK2)),iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_3488,c_3710]) ).
tcf(c_3796,plain,
( sP0(sK2,sK1)
| in(sK3(sK11(sK1,sK2)),iPr_def_12)
| ~ element(sK2,iPr_def_14)
| ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_3720,c_2671]) ).
tcf(c_3797,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3796,c_3710,c_3722,c_2674,c_3721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU310+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 13:33:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 2.28/1.28 % SZS status Started for theBenchmark.p
% 2.28/1.28 % SZS status Theorem for theBenchmark.p
% 2.28/1.28
% 2.28/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.28/1.28
% 2.28/1.28 % ------ iProver source info
% 2.28/1.28
% 2.28/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.28/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.28/1.28 % git: non_committed_changes: false
% 2.28/1.28
% 2.28/1.28 % ------ Parsing...
% 2.28/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 50 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.28/1.28
% 2.28/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.28/1.28 % ------ Proving...
% 2.28/1.28 % ------ Problem Properties
% 2.28/1.28
% 2.28/1.28 %
% 2.28/1.28 % clauses 27
% 2.28/1.28 % conjectures 4
% 2.28/1.28 % EPR 5
% 2.28/1.28 % Horn 20
% 2.28/1.28 % unary 12
% 2.28/1.28 % binary 10
% 2.28/1.28 % lits 52
% 2.28/1.29 % lits eq 9
% 2.28/1.29 % fd_pure 0
% 2.28/1.29 % fd_pseudo 0
% 2.28/1.29 % fd_cond 0
% 2.28/1.29 % fd_pseudo_cond 0
% 2.28/1.29 % AC symbols 0
% 2.28/1.29
% 2.28/1.29 % ------ Schedule dynamic 5 is on
% 2.28/1.29
% 2.28/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.28/1.29
% 2.28/1.29
% 2.28/1.29 % ------
% 2.28/1.29 % Current options:
% 2.28/1.29 % ------
% 2.28/1.29
% 2.28/1.29
% 2.28/1.29 %
% 2.28/1.29
% 2.28/1.29 % ------ Proving...
% 2.28/1.29 %
% 2.28/1.29
% 2.28/1.29 % SZS status Theorem for theBenchmark.p
% 2.28/1.29
% 2.28/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.28/1.29
% 2.28/1.29
%------------------------------------------------------------------------------