%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU311+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 : n003.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 02:56:36 PM UTC 2026
% Result : Theorem 3.30s 1.16s
% Output : CNFRefutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 84 ( 16 unt; 2 def)
% Number of atoms : 361 ( 5 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 387 ( 161 ~; 159 |; 47 &)
% ( 9 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 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 : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 124 !; 20 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f36,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f37,axiom,
! [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/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(f38,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f42,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f65,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
<~> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f66,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
<~> in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(flattening,[],[f65]) ).
fof(f88,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,[],[f37]) ).
fof(f89,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,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f95,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& ( ~ in(X3,X2)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f96,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& top_str(X0)
& topological_space(X0)
& ! [X2] :
( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& ( in(X3,X2)
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) )
& ( ~ in(X3,X2)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1) ) )
| ~ element(X2,powerset(powerset(the_carrier(X0)))) ) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
( element(sK1,powerset(powerset(the_carrier(sK0))))
& top_str(sK0)
& topological_space(sK0)
& ! [X2] :
( ( element(sK2(X2),powerset(the_carrier(sK0)))
& ( in(sK2(X2),X2)
| in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1) )
& ( ~ in(sK2(X2),X2)
| ~ in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1) ) )
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2))],[f96]) ).
fof(f102,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(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f103,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(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,X2) ) ) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ! [X3] :
( ( ~ in(X3,sK7(X0,X1))
| ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
& in(X3,powerset(the_carrier(X0))) ) )
& ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK7(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( ( ~ element(X1,X0)
| empty(X1) )
& ( ~ empty(X1)
| element(X1,X0) ) ) )
& ( empty(X0)
| ( ( ~ element(X1,X0)
| in(X1,X0) )
& ( ~ in(X1,X0)
| element(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f107,plain,
! [X0,X1] :
( ( in(sK9(X0,X1),X0)
& ~ in(sK9(X0,X1),X1) )
| element(X0,powerset(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f91]) ).
fof(f110,plain,
element(sK1,powerset(powerset(the_carrier(sK0)))),
inference(cnf_transformation,[],[f97]) ).
fof(f111,plain,
top_str(sK0),
inference(cnf_transformation,[],[f97]) ).
fof(f112,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f97]) ).
fof(f113,plain,
! [X2] :
( element(sK2(X2),powerset(the_carrier(sK0)))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f114,plain,
! [X2] :
( in(sK2(X2),X2)
| in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f115,plain,
! [X2] :
( ~ in(sK2(X2),X2)
| ~ in(set_difference(cast_as_carrier_subset(sK0),sK2(X2)),sK1)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f97]) ).
fof(f169,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f170,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK7(X0,X1))
| in(set_difference(cast_as_carrier_subset(X0),X3),X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f171,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(X3,sK7(X0,X1))
| in(X3,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f104]) ).
fof(f172,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
| ~ in(X3,powerset(the_carrier(X0)))
| in(X3,sK7(X0,X1)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f175,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f179,plain,
! [X0,X1] :
( in(sK9(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f180,plain,
! [X0,X1] :
( ~ in(sK9(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ in(sK2(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(set_difference(cast_as_carrier_subset(sK0),sK2(X0)),sK1) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(sK2(X0),X0)
| in(set_difference(cast_as_carrier_subset(sK0),sK2(X0)),sK1)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( element(sK2(X0),powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_52,negated_conjecture,
topological_space(sK0),
inference(cnf_transformation,[],[f112]) ).
tcf(c_53,negated_conjecture,
top_str(sK0),
inference(cnf_transformation,[],[f111]) ).
tcf(c_54,negated_conjecture,
element(sK1,powerset(powerset(the_carrier(sK0)))),
inference(cnf_transformation,[],[f110]) ).
tcf(c_108,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f169]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK7(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,[],[f172]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK7(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X1),X2),X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X2,sK7(X1,X0))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ in(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| in(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_846,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(set_difference(cast_as_carrier_subset(X0),X2),X1)
| ~ top_str(X0)
| ~ in(X2,sK7(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_111]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(sK0),X1),X0)
| ~ top_str(sK0)
| ~ in(X1,sK7(sK0,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_846]) ).
tcf(c_849,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(sK0),X1),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(X1,sK7(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_847,c_53,c_847]) ).
tcf(c_850,plain,
! [X0: $i,X1: $i] :
( in(set_difference(cast_as_carrier_subset(sK0),X1),X0)
| ~ in(X1,sK7(sK0,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(renaming,[status(thm)],[c_849]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ in(X2,sK7(X0,X1))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_110]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ in(X1,sK7(sK0,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_861]) ).
tcf(c_864,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(X1,sK7(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_862,c_53,c_862]) ).
tcf(c_865,plain,
! [X0: $i,X1: $i] :
( in(X1,powerset(the_carrier(sK0)))
| ~ in(X1,sK7(sK0,X0))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(renaming,[status(thm)],[c_864]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,sK7(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 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_109]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i] :
( in(X0,sK7(sK0,X1))
| ~ top_str(sK0)
| ~ in(X0,powerset(the_carrier(sK0)))
| ~ element(X1,powerset(powerset(the_carrier(sK0))))
| ~ in(set_difference(cast_as_carrier_subset(sK0),X0),X1) ),
inference(unflattening,[status(thm)],[c_876]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i] :
( in(X0,sK7(sK0,X1))
| ~ in(set_difference(cast_as_carrier_subset(sK0),X0),X1)
| ~ element(X1,powerset(powerset(the_carrier(sK0))))
| ~ in(X0,powerset(the_carrier(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_877,c_53,c_877]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i] :
( in(X0,sK7(sK0,X1))
| ~ in(X0,powerset(the_carrier(sK0)))
| ~ element(X1,powerset(powerset(the_carrier(sK0))))
| ~ in(set_difference(cast_as_carrier_subset(sK0),X0),X1) ),
inference(renaming,[status(thm)],[c_879]) ).
tcf(c_1136,definition,
iPr_def_12 = powerset(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1138,definition,
iPr_def_14 = powerset(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i] :
( in(X0,sK7(sK0,X1))
| ~ in(X0,iPr_def_12)
| ~ element(X1,iPr_def_14)
| ~ in(set_difference(iPr_def_10,X0),X1) ),
inference(demodulation,[status(thm)],[c_880,c_1138]) ).
tcf(c_1142,plain,
! [X0: $i,X1: $i] :
( in(X0,iPr_def_12)
| ~ element(X1,iPr_def_14)
| ~ in(X0,sK7(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_865]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i] :
( in(set_difference(iPr_def_10,X0),X1)
| ~ element(X1,iPr_def_14)
| ~ in(X0,sK7(sK0,X1)) ),
inference(demodulation,[status(thm)],[c_850]) ).
tcf(c_1144,negated_conjecture,
element(sK1,iPr_def_14),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_1145,negated_conjecture,
! [X0: $i] :
( element(sK2(X0),iPr_def_12)
| ~ element(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_1146,negated_conjecture,
! [X0: $i] :
( in(sK2(X0),X0)
| in(set_difference(iPr_def_10,sK2(X0)),sK1)
| ~ element(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_1147,negated_conjecture,
! [X0: $i] :
( ~ element(X0,iPr_def_14)
| ~ in(sK2(X0),X0)
| ~ in(set_difference(iPr_def_10,sK2(X0)),sK1) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_1634,plain,
! [X0: $i] :
( in(set_difference(iPr_def_10,sK2(sK7(sK0,X0))),sK1)
| in(set_difference(iPr_def_10,sK2(sK7(sK0,X0))),X0)
| ~ element(X0,iPr_def_14)
| ~ element(sK7(sK0,X0),iPr_def_14) ),
inference(superposition,[status(thm)],[c_1146,c_1143]) ).
tcf(c_1659,plain,
( in(set_difference(iPr_def_10,sK2(sK7(sK0,sK1))),sK1)
| ~ element(sK1,iPr_def_14)
| ~ element(sK7(sK0,sK1),iPr_def_14) ),
inference(equality_factoring,[status(thm)],[c_1634]) ).
tcf(c_1661,plain,
( in(set_difference(iPr_def_10,sK2(sK7(sK0,sK1))),sK1)
| ~ element(sK7(sK0,sK1),iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1659,c_1144]) ).
tcf(c_1692,plain,
( ~ element(sK7(sK0,sK1),iPr_def_14)
| ~ in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_1661,c_1147]) ).
tcf(c_1710,plain,
( in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1))
| ~ element(sK1,iPr_def_14)
| ~ element(sK7(sK0,sK1),iPr_def_14)
| ~ in(sK2(sK7(sK0,sK1)),iPr_def_12) ),
inference(superposition,[status(thm)],[c_1661,c_1141]) ).
tcf(c_1721,plain,
( in(sK2(sK7(sK0,sK1)),sK7(sK0,sK1))
| ~ element(sK7(sK0,sK1),iPr_def_14)
| ~ in(sK2(sK7(sK0,sK1)),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1710,c_1144]) ).
tcf(c_1741,plain,
~ empty(iPr_def_12),
inference(superposition,[status(thm)],[c_1136,c_108]) ).
tcf(c_1795,plain,
( ~ in(sK2(sK7(sK0,sK1)),iPr_def_12)
| ~ element(sK7(sK0,sK1),iPr_def_14) ),
inference(global_subsumption_just,[status(thm)],[c_1721,c_1692,c_1721]) ).
tcf(c_1796,plain,
( ~ element(sK7(sK0,sK1),iPr_def_14)
| ~ in(sK2(sK7(sK0,sK1)),iPr_def_12) ),
inference(renaming,[status(thm)],[c_1795]) ).
tcf(c_2199,plain,
! [X0: $i] :
( empty(iPr_def_12)
| in(sK2(X0),iPr_def_12)
| ~ element(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_1145,c_113]) ).
tcf(c_2220,plain,
! [X0: $i] :
( in(sK2(X0),iPr_def_12)
| ~ element(X0,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2199,c_1741]) ).
tcf(c_2315,plain,
~ element(sK7(sK0,sK1),iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_1796,c_2220]) ).
tcf(c_2472,plain,
! [X0: $i,X1: $i] :
( element(sK7(sK0,X0),powerset(X1))
| in(sK9(sK7(sK0,X0),X1),iPr_def_12)
| ~ element(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_119,c_1142]) ).
tcf(c_3775,plain,
! [X0: $i] :
( element(sK7(sK0,X0),powerset(iPr_def_12))
| ~ element(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_2472,c_118]) ).
tcf(c_3776,plain,
! [X0: $i] :
( element(sK7(sK0,X0),iPr_def_14)
| ~ element(X0,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_3775,c_1138]) ).
tcf(c_3976,plain,
~ element(sK1,iPr_def_14),
inference(superposition,[status(thm)],[c_3776,c_2315]) ).
tcf(c_3977,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3976,c_1144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.34 % Computer : n003.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Thu Sep 24 13:40:36 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 Running first-order theorem proving
% 0.10/0.37 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
% 0.12/0.38
% 0.12/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.38
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 3.30/1.16 % SZS status Started for theBenchmark.p
% 3.30/1.16 % SZS status Theorem for theBenchmark.p
% 3.30/1.16
% 3.30/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.30/1.16
% 3.30/1.16 % ------ iProver source info
% 3.30/1.16
% 3.30/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 3.30/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.30/1.16 % git: non_committed_changes: false
% 3.30/1.16
% 3.30/1.16 % ------ Parsing...
% 3.30/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.30/1.16
% 3.30/1.16 % ------ 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 %
% 3.30/1.16
% 3.30/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.30/1.16
% 3.30/1.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.30/1.16 % ------ Proving...
% 3.30/1.16 % ------ Problem Properties
% 3.30/1.16
% 3.30/1.16 %
% 3.30/1.16 % clauses 34
% 3.30/1.16 % conjectures 4
% 3.30/1.16 % EPR 15
% 3.30/1.16 % Horn 30
% 3.30/1.16 % unary 16
% 3.30/1.16 % binary 9
% 3.30/1.16 % lits 62
% 3.30/1.16 % lits eq 7
% 3.30/1.16 % fd_pure 0
% 3.30/1.16 % fd_pseudo 0
% 3.30/1.16 % fd_cond 1
% 3.30/1.16 % fd_pseudo_cond 1
% 3.30/1.16 % AC symbols 0
% 3.30/1.16
% 3.30/1.16 % ------ Schedule dynamic 5 is on
% 3.30/1.16
% 3.30/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.30/1.16
% 3.30/1.16
% 3.30/1.16 % ------
% 3.30/1.16 % Current options:
% 3.30/1.16 % ------
% 3.30/1.16
% 3.30/1.16
% 3.30/1.16 %
% 3.30/1.16
% 3.30/1.16 % ------ Proving...
% 3.30/1.16 %
% 3.30/1.16
% 3.30/1.16 % SZS status Theorem for theBenchmark.p
% 3.30/1.16
% 3.30/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.30/1.16
% 3.30/1.16
%------------------------------------------------------------------------------