%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU111+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 02:55:26 PM UTC 2026
% Result : Theorem 10.76s 2.75s
% Output : CNFRefutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 95 ( 13 unt; 0 def)
% Number of atoms : 345 ( 37 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 413 ( 163 ~; 188 |; 50 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 188 ( 0 sgn 178 !; 10 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f11,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f12,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f34,axiom,
! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(f35,conjecture,
! [X0,X1] : finite_subsets(set_intersection2(X0,X1)) = set_intersection2(finite_subsets(X0),finite_subsets(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finsub_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1] : finite_subsets(set_intersection2(X0,X1)) = set_intersection2(finite_subsets(X0),finite_subsets(X1)),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f63,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(ennf_transformation,[],[f32]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f73,plain,
? [X0,X1] : finite_subsets(set_intersection2(X0,X1)) != set_intersection2(finite_subsets(X0),finite_subsets(X1)),
inference(ennf_transformation,[],[f36]) ).
fof(f84,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f85,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK1(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ finite(X2)
| ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f92,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ finite(X2)
| ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| ( finite(X3)
& subset(X3,X0) ) )
& ( ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ( finite(X2)
& subset(X2,X0) ) )
& ( ~ in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ preboolean(X1)
| ( ( finite_subsets(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| ( finite(X3)
& subset(X3,X0) ) )
& ( ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| ( finite(sK2(X0,X1))
& subset(sK2(X0,X1),X0) ) )
& ( ~ in(sK2(X0,X1),X1)
| ~ finite(sK2(X0,X1))
| ~ subset(sK2(X0,X1),X0) ) )
| X1 = finite_subsets(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f93]) ).
fof(f105,plain,
finite_subsets(set_intersection2(sK13,sK14)) != set_intersection2(finite_subsets(sK13),finite_subsets(sK14)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f73]) ).
fof(f118,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f119,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f120,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f121,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f122,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f124,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f125,plain,
! [X2,X0,X1] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f127,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ in(X3,X1)
| finite(X3) ),
inference(cnf_transformation,[],[f94]) ).
fof(f128,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f129,plain,
! [X3,X0,X1] :
( ~ preboolean(X1)
| finite_subsets(X0) != X1
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f133,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f173,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f174,plain,
finite_subsets(set_intersection2(sK13,sK14)) != set_intersection2(finite_subsets(sK13),finite_subsets(sK14)),
inference(cnf_transformation,[],[f105]) ).
fof(f187,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f122]) ).
fof(f188,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f121]) ).
fof(f189,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0)
| in(X3,finite_subsets(X0)) ),
inference(equality_resolution,[],[f129]) ).
fof(f190,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X3,finite_subsets(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f191,plain,
! [X3,X0] :
( ~ preboolean(finite_subsets(X0))
| ~ in(X3,finite_subsets(X0))
| finite(X3) ),
inference(equality_resolution,[],[f127]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK1(X0,X1,X2),X2)
| in(sK1(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ preboolean(finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ preboolean(finite_subsets(X1))
| ~ in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ preboolean(finite_subsets(X1))
| ~ in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_75,plain,
! [X0: $i] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f133]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( subset(finite_subsets(X0),finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_116,negated_conjecture,
set_intersection2(finite_subsets(sK13),finite_subsets(sK14)) != finite_subsets(set_intersection2(sK13,sK14)),
inference(cnf_transformation,[],[f174]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ in(X0,finite_subsets(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_74,c_75]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( in(X0,finite_subsets(X1))
| ~ finite(X0)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_72,c_75]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_73,c_75]) ).
tcf(c_1123,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_379]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(renaming,[status(thm)],[c_1123]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,finite_subsets(X1))
| finite(X0) ),
inference(prop_impl_just,[status(thm)],[c_377]) ).
tcf(c_1138,plain,
! [X0: $i,X1: $i] :
( finite(X0)
| ~ in(X0,finite_subsets(X1)) ),
inference(renaming,[status(thm)],[c_1137]) ).
tcf(c_2943,plain,
( ( set_intersection2(finite_subsets(sK13),finite_subsets(sK14)) = finite_subsets(set_intersection2(sK13,sK14)) )
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14))
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(set_intersection2(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2962,plain,
! [X0: $i] :
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14))
| ~ subset(X0,finite_subsets(sK14))
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_3003,plain,
! [X0: $i] :
( finite(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))))
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(X0)) ),
inference(instantiation,[status(thm)],[c_1138]) ).
tcf(c_3023,plain,
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(set_intersection2(sK13,sK14)))
| ~ finite(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))))
| ~ subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14)) ),
inference(instantiation,[status(thm)],[c_378]) ).
tcf(c_3090,plain,
( subset(finite_subsets(set_intersection2(sK13,sK14)),finite_subsets(sK14))
| ~ subset(set_intersection2(sK13,sK14),sK14) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_3169,plain,
! [X0: $i] :
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14))
| ~ subset(finite_subsets(X0),finite_subsets(sK14))
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(X0)) ),
inference(instantiation,[status(thm)],[c_2962]) ).
tcf(c_3356,plain,
( finite(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))))
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14)) ),
inference(instantiation,[status(thm)],[c_3003]) ).
tcf(c_3357,plain,
! [X0: $i] :
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(X0))
| ~ finite(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))))
| ~ subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0) ),
inference(instantiation,[status(thm)],[c_378]) ).
tcf(c_3360,plain,
( subset(set_intersection2(sK13,sK14),sK14)
| ~ in(sK0(set_intersection2(sK13,sK14),sK14),sK14) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_3361,plain,
( subset(set_intersection2(sK13,sK14),sK14)
| in(sK0(set_intersection2(sK13,sK14),sK14),set_intersection2(sK13,sK14)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3705,plain,
( subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),sK14)
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14)) ),
inference(instantiation,[status(thm)],[c_1124]) ).
tcf(c_3722,plain,
( subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14))
| ~ subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),sK14)
| ~ subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),sK13) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_4514,plain,
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14))
| ~ subset(finite_subsets(set_intersection2(sK13,sK14)),finite_subsets(sK14))
| ~ in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(set_intersection2(sK13,sK14))) ),
inference(instantiation,[status(thm)],[c_3169]) ).
tcf(c_6743,plain,
( in(sK0(set_intersection2(sK13,sK14),sK14),sK14)
| ~ in(sK0(set_intersection2(sK13,sK14),sK14),set_intersection2(sK13,sK14)) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_14825,plain,
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(set_intersection2(sK13,sK14))) ),
inference(resolution,[status(thm)],[c_64,c_116]) ).
tcf(c_15270,plain,
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14))
| in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(set_intersection2(sK13,sK14))) ),
inference(resolution,[status(thm)],[c_65,c_116]) ).
tcf(c_16140,plain,
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14)) ),
inference(resolution,[status(thm)],[c_14825,c_1124]) ).
tcf(c_16380,plain,
in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK14)),
inference(global_subsumption_just,[status(thm)],[c_15270,c_3090,c_3361,c_3360,c_4514,c_6743,c_15270]) ).
tcf(c_16614,plain,
( in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| ~ finite(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))))
| ~ subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),sK13) ),
inference(instantiation,[status(thm)],[c_3357]) ).
tcf(c_16758,plain,
! [X0: $i] :
( in(X0,set_intersection2(sK13,sK14))
| in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| ~ in(X0,sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14)))) ),
inference(resolution,[status(thm)],[c_16140,c_62]) ).
tcf(c_16991,plain,
! [X0: $i] :
( subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0)
| in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| in(sK0(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0),set_intersection2(sK13,sK14)) ),
inference(resolution,[status(thm)],[c_16758,c_61]) ).
tcf(c_17223,plain,
! [X0: $i] :
( subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0)
| in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| in(sK0(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0),sK13) ),
inference(resolution,[status(thm)],[c_16991,c_67]) ).
tcf(c_17224,plain,
! [X0: $i] :
( subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0)
| in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13))
| in(sK0(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),X0),sK14) ),
inference(resolution,[status(thm)],[c_16991,c_68]) ).
tcf(c_33423,plain,
( subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),sK13)
| in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13)) ),
inference(resolution,[status(thm)],[c_17223,c_60]) ).
tcf(c_33451,plain,
in(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),finite_subsets(sK13)),
inference(global_subsumption_just,[status(thm)],[c_17224,c_3356,c_16380,c_16614,c_33423]) ).
tcf(c_33460,plain,
subset(sK1(finite_subsets(sK13),finite_subsets(sK14),finite_subsets(set_intersection2(sK13,sK14))),sK13),
inference(resolution,[status(thm)],[c_33451,c_1124]) ).
tcf(c_33461,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_33460,c_33451,c_16380,c_3722,c_3705,c_3356,c_3023,c_2943,c_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU111+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:49:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 10.76/2.75 % SZS status Started for theBenchmark.p
% 10.76/2.75 % SZS status Theorem for theBenchmark.p
% 10.76/2.75
% 10.76/2.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.76/2.75
% 10.76/2.75 % ------ iProver source info
% 10.76/2.75
% 10.76/2.75 % git: date: 2026-07-19 20:42:38 +0200
% 10.76/2.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.76/2.75 % git: non_committed_changes: false
% 10.76/2.75
% 10.76/2.75 % ------ Parsing...
% 10.76/2.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.76/2.75
% 10.76/2.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 10.76/2.75
% 10.76/2.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.76/2.75
% 10.76/2.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.76/2.75 % ------ Proving...
% 10.76/2.75 % ------ Problem Properties
% 10.76/2.75
% 10.76/2.75 %
% 10.76/2.75 % clauses 64
% 10.76/2.75 % conjectures 1
% 10.76/2.75 % EPR 20
% 10.76/2.75 % Horn 53
% 10.76/2.75 % unary 23
% 10.76/2.75 % binary 25
% 10.76/2.75 % lits 126
% 10.76/2.75 % lits eq 13
% 10.76/2.75 % fd_pure 0
% 10.76/2.75 % fd_pseudo 0
% 10.76/2.75 % fd_cond 1
% 10.76/2.75 % fd_pseudo_cond 8
% 10.76/2.75 % AC symbols 0
% 10.76/2.75
% 10.76/2.75 % ------ Input Options Time Limit: Unbounded
% 10.76/2.75
% 10.76/2.75
% 10.76/2.75 % ------
% 10.76/2.75 % Current options:
% 10.76/2.75 % ------
% 10.76/2.75
% 10.76/2.75
% 10.76/2.75 %
% 10.76/2.75
% 10.76/2.75 % ------ Proving...
% 10.76/2.75 %
% 10.76/2.75
% 10.76/2.75 % SZS status Theorem for theBenchmark.p
% 10.76/2.75
% 10.76/2.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.76/2.75
% 10.76/2.75
%------------------------------------------------------------------------------