%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET948+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:49:11 PM UTC 2026
% Result : Theorem 61.98s 11.36s
% Output : CNFRefutation 61.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 114 ( 10 unt; 0 def)
% Number of atoms : 457 ( 75 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 577 ( 234 ~; 248 |; 81 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 271 ( 0 sgn 249 !; 22 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f8,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f17,conjecture,
! [X0,X1] :
( ! [X2,X3] :
( ( in(X3,set_union2(X0,X1))
& in(X2,set_union2(X0,X1)) )
=> ( disjoint(X2,X3)
| X2 = X3 ) )
=> union(set_intersection2(X0,X1)) = set_intersection2(union(X0),union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ! [X2,X3] :
( ( in(X3,set_union2(X0,X1))
& in(X2,set_union2(X0,X1)) )
=> ( disjoint(X2,X3)
| X2 = X3 ) )
=> union(set_intersection2(X0,X1)) = set_intersection2(union(X0),union(X1)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
fof(f23,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X3] : in(X3,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f25,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ in(X3,set_union2(X0,X1))
| ~ in(X2,set_union2(X0,X1))
| disjoint(X2,X3)
| X2 = X3 )
& union(set_intersection2(X0,X1)) != set_intersection2(union(X0),union(X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f26,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ in(X3,set_union2(X0,X1))
| ~ in(X2,set_union2(X0,X1))
| disjoint(X2,X3)
| X2 = X3 )
& union(set_intersection2(X0,X1)) != set_intersection2(union(X0),union(X1)) ),
inference(flattening,[],[f25]) ).
fof(f30,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( ? [X2] : in(X2,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
( ! [X2,X3] :
( ~ in(X3,set_union2(sK0,sK1))
| ~ in(X2,set_union2(sK0,sK1))
| disjoint(X2,X3)
| X2 = X3 )
& union(set_intersection2(sK0,sK1)) != set_intersection2(union(sK0),union(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f26]) ).
fof(f34,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,[],[f7]) ).
fof(f35,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,[],[f34]) ).
fof(f36,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,[],[f35]) ).
fof(f37,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(sK2(X0,X1,X2),X2)
| ( in(sK2(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0) ) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( set_union2(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_union2(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK3(X0,X1,X2),X2)
| in(sK3(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X0) )
& ( ~ in(sK3(X0,X1,X2),X2)
| ( ~ in(sK3(X0,X1,X2),X1)
& ~ in(sK3(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f43,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK6(X0,X5),X0)
& in(X5,sK6(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK4(X0,X1),X1)
| ( in(sK5(X0,X1),X0)
& in(sK4(X0,X1),sK5(X0,X1)) ) )
& ( ~ in(sK4(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK4(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ( in(sK7(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f30]) ).
fof(f48,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,[],[f32]) ).
fof(f49,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,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK10(X0,X1),X0)
& ~ in(sK10(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X2,X3] :
( ~ in(X3,set_union2(sK0,sK1))
| ~ in(X2,set_union2(sK0,sK1))
| disjoint(X2,X3)
| X2 = X3 ),
inference(cnf_transformation,[],[f33]) ).
fof(f54,plain,
union(set_intersection2(sK0,sK1)) != set_intersection2(union(sK0),union(sK1)),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f61,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f37]) ).
fof(f64,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f65,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f74,plain,
! [X0,X1] : subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
inference(cnf_transformation,[],[f20]) ).
fof(f75,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK6(X0,X5),X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f76,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(X5,sK6(X0,X5)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f77,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f81,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f90,plain,
! [X0,X1] :
( X0 != X1
| subset(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f92,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f52]) ).
fof(f93,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f59]) ).
fof(f94,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f58]) ).
fof(f95,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f57]) ).
fof(f96,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f65]) ).
fof(f97,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f64]) ).
fof(f99,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f77]) ).
fof(f100,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK6(X0,X5)) ),
inference(equality_resolution,[],[f76]) ).
fof(f101,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK6(X0,X5),X0) ),
inference(equality_resolution,[],[f75]) ).
fof(f103,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f90]) ).
tcf(c_49,negated_conjecture,
set_intersection2(union(sK0),union(sK1)) != union(set_intersection2(sK0,sK1)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( X0 = X1 )
| ~ in(X1,set_union2(sK0,sK1))
| ~ in(X0,set_union2(sK0,sK1)) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(X0,X1) = X2 )
| ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X1)
| ( set_intersection2(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : subset(union(set_intersection2(X0,X1)),set_intersection2(union(X0),union(X1))),
inference(cnf_transformation,[],[f74]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( in(X0,sK6(X1,X0))
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( in(sK6(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_88,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f103]) ).
tcf(c_89,plain,
subset(sK0,sK0),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_102,plain,
( ( sK0 = sK0 )
| ~ subset(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_779,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1654,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK0))
| in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(set_intersection2(sK0,sK1)))
| ( set_intersection2(union(sK0),union(sK1)) = union(set_intersection2(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1669,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK1))
| in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(set_intersection2(sK0,sK1)))
| ( set_intersection2(union(sK0),union(sK1)) = union(set_intersection2(sK0,sK1)) ) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1689,plain,
( ( set_intersection2(union(sK0),union(sK1)) = union(set_intersection2(sK0,sK1)) )
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK1))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK0))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(set_intersection2(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1715,plain,
! [X0: $i] :
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),X0)
| ~ subset(union(set_intersection2(sK0,sK1)),X0)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(set_intersection2(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2218,plain,
subset(union(set_intersection2(sK0,sK1)),set_intersection2(union(sK0),union(sK1))),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_2278,plain,
( in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK0)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_2279,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK0)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_2571,plain,
( in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK1)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK1)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_2572,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK1)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_5161,plain,
! [X0: $i] :
( in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_union2(sK0,X0))
| ~ in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_5165,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ~ in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0)
| ( X1 != sK0 )
| ( X0 != sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) ) ),
inference(instantiation,[status(thm)],[c_779]) ).
tcf(c_5280,plain,
! [X0: $i] :
( in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_union2(X0,sK1))
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_5284,plain,
( in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_union2(sK0,sK1))
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK1) ),
inference(instantiation,[status(thm)],[c_5280]) ).
tcf(c_5458,plain,
! [X0: $i] :
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),X0))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),X0)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_5460,plain,
! [X0: $i] :
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(X0))
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),X0)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_9435,plain,
! [X0: $i] :
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),X0)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(union(sK0),X0)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_10049,plain,
! [X0: $i,X1: $i] :
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(X0,X1))
| ~ subset(union(set_intersection2(sK0,sK1)),set_intersection2(X0,X1))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(set_intersection2(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_1715]) ).
tcf(c_10050,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X0,X1)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(X0,X1)) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_10052,plain,
! [X0: $i,X1: $i] :
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),X0)
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(X0,X1)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_21444,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))))))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_5458]) ).
tcf(c_22561,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(set_intersection2(sK0,sK1)))
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_intersection2(sK0,sK1))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_5460]) ).
tcf(c_26908,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK1))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(union(sK0),union(sK1))) ),
inference(instantiation,[status(thm)],[c_9435]) ).
tcf(c_31962,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(sK0))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(union(sK0),union(sK1))) ),
inference(instantiation,[status(thm)],[c_10052]) ).
tcf(c_57253,plain,
! [X0: $i] :
( disjoint(X0,sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))
| ( X0 = sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) )
| ~ in(X0,set_union2(sK0,sK1))
| ~ in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_union2(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_61011,plain,
( in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(union(sK0),union(sK1)))
| ~ subset(union(set_intersection2(sK0,sK1)),set_intersection2(union(sK0),union(sK1)))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),union(set_intersection2(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_10049]) ).
tcf(c_62844,plain,
! [X0: $i] :
( ~ disjoint(X0,sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(X0,sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))) ),
inference(instantiation,[status(thm)],[c_10050]) ).
tcf(c_62919,plain,
( in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_union2(sK0,sK1))
| ~ in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0) ),
inference(instantiation,[status(thm)],[c_5161]) ).
tcf(c_87282,plain,
( disjoint(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))
| ( sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) = sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) )
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_union2(sK0,sK1))
| ~ in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_union2(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_57253]) ).
tcf(c_110477,plain,
! [X0: $i] :
( in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),X0)
| ~ in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0)
| ( X0 != sK0 )
| ( sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) != sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) ) ),
inference(instantiation,[status(thm)],[c_5165]) ).
tcf(c_110478,plain,
( in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0)
| ~ in(sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0)
| ( sK0 != sK0 )
| ( sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) != sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))) ) ),
inference(instantiation,[status(thm)],[c_110477]) ).
tcf(c_173847,plain,
( ~ disjoint(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))
| ~ in(sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1))),set_intersection2(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK6(sK0,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))))) ),
inference(instantiation,[status(thm)],[c_62844]) ).
tcf(c_183508,plain,
! [X0: $i] :
( in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_intersection2(X0,sK1))
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK1)
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_183509,plain,
( in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),set_intersection2(sK0,sK1))
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK1)
| ~ in(sK6(sK1,sK2(union(sK0),union(sK1),union(set_intersection2(sK0,sK1)))),sK0) ),
inference(instantiation,[status(thm)],[c_183508]) ).
tcf(c_183510,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_183509,c_173847,c_110478,c_87282,c_62919,c_61011,c_31962,c_26908,c_22561,c_21444,c_5284,c_2571,c_2572,c_2278,c_2279,c_2218,c_1689,c_1669,c_1654,c_102,c_49,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET948+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:24:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 61.98/11.36 % SZS status Started for theBenchmark.p
% 61.98/11.36 % SZS status Theorem for theBenchmark.p
% 61.98/11.36
% 61.98/11.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 61.98/11.36
% 61.98/11.36 % ------ iProver source info
% 61.98/11.36
% 61.98/11.36 % git: date: 2026-07-19 20:42:38 +0200
% 61.98/11.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 61.98/11.36 % git: non_committed_changes: false
% 61.98/11.36
% 61.98/11.36 % ------ Parsing...
% 61.98/11.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 61.98/11.36
% 61.98/11.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 61.98/11.36
% 61.98/11.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 61.98/11.36
% 61.98/11.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 61.98/11.36 % ------ Proving...
% 61.98/11.36 % ------ Problem Properties
% 61.98/11.36
% 61.98/11.36 %
% 61.98/11.36 % clauses 38
% 61.98/11.36 % conjectures 2
% 61.98/11.36 % EPR 7
% 61.98/11.36 % Horn 29
% 61.98/11.36 % unary 9
% 61.98/11.36 % binary 14
% 61.98/11.36 % lits 86
% 61.98/11.36 % lits eq 16
% 61.98/11.36 % fd_pure 0
% 61.98/11.36 % fd_pseudo 0
% 61.98/11.36 % fd_cond 0
% 61.98/11.36 % fd_pseudo_cond 11
% 61.98/11.36 % AC symbols 0
% 61.98/11.36
% 61.98/11.36 % ------ Schedule dynamic 5 is on
% 61.98/11.36
% 61.98/11.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 61.98/11.36
% 61.98/11.36
% 61.98/11.36 % ------
% 61.98/11.36 % Current options:
% 61.98/11.36 % ------
% 61.98/11.36
% 61.98/11.36
% 61.98/11.36 %
% 61.98/11.36
% 61.98/11.36 % ------ Proving...
% 61.98/11.36 % Proof_search_loop: time out after: 3891 full_loop iterations
% 61.98/11.36
% 61.98/11.36 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 61.98/11.36
% 61.98/11.36
% 61.98/11.36 % ------
% 61.98/11.36 % Current options:
% 61.98/11.36 % ------
% 61.98/11.36
% 61.98/11.36
% 61.98/11.36 %
% 61.98/11.36
% 61.98/11.36 % ------ Proving...
% 61.98/11.36 %
% 61.98/11.36
% 61.98/11.36 % SZS status Theorem for theBenchmark.p
% 61.98/11.36
% 61.98/11.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.98/11.36
% 61.98/11.36
%------------------------------------------------------------------------------