%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT294+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 01:59:08 PM UTC 2026
% Result : Theorem 3.49s 1.28s
% Output : CNFRefutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 125 ( 73 unt; 5 def)
% Number of atoms : 843 ( 42 equ)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 1060 ( 464 ~; 468 |; 100 &)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 6 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 128 !; 12 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(X0))
& ~ v1_xboole_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X4) )
=> ! [X5] :
( ( m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X5) )
=> ( ( r6_binop_1(X0,X2,X3)
& X5 = k1_realset1(X3,X1)
& X4 = k1_realset1(X2,X1) )
=> r6_binop_1(X1,X4,X5) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(X0))
& ~ v1_xboole_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X4) )
=> ! [X5] :
( ( m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X5) )
=> ( ( r6_binop_1(X0,X2,X3)
& X5 = k1_realset1(X3,X1)
& X4 = k1_realset1(X2,X1) )
=> r6_binop_1(X1,X4,X5) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [X0,X1] :
( ( m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2) )
=> ( r6_binop_1(X0,X1,X2)
<=> ( r5_binop_1(X0,X1,X2)
& r4_binop_1(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_binop_1) ).
fof(f37,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(X0))
& ~ v1_xboole_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X3) )
=> ! [X4] :
( ( m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X4) )
=> ! [X5] :
( ( m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X5) )
=> ( ( X5 = k1_realset1(X3,X1)
& X4 = k1_realset1(X2,X1) )
=> ( ( r5_binop_1(X0,X2,X3)
=> r5_binop_1(X1,X4,X5) )
& ( r4_binop_1(X0,X2,X3)
=> r4_binop_1(X1,X4,X5) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_2) ).
fof(f48,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
& ~ v1_xboole_0(X1)
& ? [X2] :
( m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2)
& ? [X3] :
( m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X3)
& ? [X4] :
( m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X4)
& ? [X5] :
( m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X5)
& r6_binop_1(X0,X2,X3)
& X5 = k1_realset1(X3,X1)
& X4 = k1_realset1(X2,X1)
& ~ r6_binop_1(X1,X4,X5) ) ) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f49,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
& ~ v1_xboole_0(X1)
& ? [X2] :
( m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X2)
& ? [X3] :
( m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
& v1_funct_1(X3)
& ? [X4] :
( m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X4)
& ? [X5] :
( m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
& v1_funct_1(X5)
& r6_binop_1(X0,X2,X3)
& X5 = k1_realset1(X3,X1)
& X4 = k1_realset1(X2,X1)
& ~ r6_binop_1(X1,X4,X5) ) ) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f55,plain,
! [X0,X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ! [X2] :
( ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ( r6_binop_1(X0,X1,X2)
<=> ( r5_binop_1(X0,X1,X2)
& r4_binop_1(X0,X1,X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,plain,
! [X0,X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ! [X2] :
( ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ( r6_binop_1(X0,X1,X2)
<=> ( r5_binop_1(X0,X1,X2)
& r4_binop_1(X0,X1,X2) ) ) ) ),
inference(flattening,[],[f55]) ).
fof(f71,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ! [X2] :
( ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ! [X3] :
( ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ! [X4] :
( ~ m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ! [X5] :
( ~ m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X5)
| k1_realset1(X3,X1) != X5
| k1_realset1(X2,X1) != X4
| ( ( ~ r5_binop_1(X0,X2,X3)
| r5_binop_1(X1,X4,X5) )
& ( ~ r4_binop_1(X0,X2,X3)
| r4_binop_1(X1,X4,X5) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f72,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ! [X2] :
( ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ! [X3] :
( ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ! [X4] :
( ~ m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ! [X5] :
( ~ m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X5)
| k1_realset1(X3,X1) != X5
| k1_realset1(X2,X1) != X4
| ( ( ~ r5_binop_1(X0,X2,X3)
| r5_binop_1(X1,X4,X5) )
& ( ~ r4_binop_1(X0,X2,X3)
| r4_binop_1(X1,X4,X5) ) ) ) ) ) ) ) ),
inference(flattening,[],[f71]) ).
fof(f80,plain,
( ~ v1_xboole_0(sK0)
& m1_subset_1(sK1,k1_zfmisc_1(sK0))
& ~ v1_xboole_0(sK1)
& m2_relset_1(sK2,k2_zfmisc_1(sK0,sK0),sK0)
& v1_funct_2(sK2,k2_zfmisc_1(sK0,sK0),sK0)
& v1_funct_1(sK2)
& m2_relset_1(sK3,k2_zfmisc_1(sK0,sK0),sK0)
& v1_funct_2(sK3,k2_zfmisc_1(sK0,sK0),sK0)
& v1_funct_1(sK3)
& m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK4)
& m2_relset_1(sK5,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_2(sK5,k2_zfmisc_1(sK1,sK1),sK1)
& v1_funct_1(sK5)
& r6_binop_1(sK0,sK2,sK3)
& sK5 = k1_realset1(sK3,sK1)
& sK4 = k1_realset1(sK2,sK1)
& ~ r6_binop_1(sK1,sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f49]) ).
fof(f81,plain,
! [X0,X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ! [X2] :
( ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ( ( ~ r6_binop_1(X0,X1,X2)
| ( r5_binop_1(X0,X1,X2)
& r4_binop_1(X0,X1,X2) ) )
& ( ~ r5_binop_1(X0,X1,X2)
| ~ r4_binop_1(X0,X1,X2)
| r6_binop_1(X0,X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f82,plain,
! [X0,X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ! [X2] :
( ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ( ( ~ r6_binop_1(X0,X1,X2)
| ( r5_binop_1(X0,X1,X2)
& r4_binop_1(X0,X1,X2) ) )
& ( ~ r5_binop_1(X0,X1,X2)
| ~ r4_binop_1(X0,X1,X2)
| r6_binop_1(X0,X1,X2) ) ) ) ),
inference(flattening,[],[f81]) ).
fof(f94,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f95,plain,
m1_subset_1(sK1,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f80]) ).
fof(f96,plain,
~ v1_xboole_0(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f97,plain,
m2_relset_1(sK2,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f98,plain,
v1_funct_2(sK2,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f99,plain,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f80]) ).
fof(f100,plain,
m2_relset_1(sK3,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f101,plain,
v1_funct_2(sK3,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f102,plain,
v1_funct_1(sK3),
inference(cnf_transformation,[],[f80]) ).
fof(f103,plain,
m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f104,plain,
v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f105,plain,
v1_funct_1(sK4),
inference(cnf_transformation,[],[f80]) ).
fof(f106,plain,
m2_relset_1(sK5,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f107,plain,
v1_funct_2(sK5,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f108,plain,
v1_funct_1(sK5),
inference(cnf_transformation,[],[f80]) ).
fof(f109,plain,
r6_binop_1(sK0,sK2,sK3),
inference(cnf_transformation,[],[f80]) ).
fof(f110,plain,
sK5 = k1_realset1(sK3,sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f111,plain,
sK4 = k1_realset1(sK2,sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
~ r6_binop_1(sK1,sK4,sK5),
inference(cnf_transformation,[],[f80]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ r6_binop_1(X0,X1,X2)
| r5_binop_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ r6_binop_1(X0,X1,X2)
| r4_binop_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ r5_binop_1(X0,X1,X2)
| ~ r4_binop_1(X0,X1,X2)
| r6_binop_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f153,plain,
! [X2,X3,X0,X1,X4,X5] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ~ m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ~ m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X5)
| k1_realset1(X3,X1) != X5
| k1_realset1(X2,X1) != X4
| ~ r5_binop_1(X0,X2,X3)
| r5_binop_1(X1,X4,X5) ),
inference(cnf_transformation,[],[f72]) ).
fof(f154,plain,
! [X2,X3,X0,X1,X4,X5] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ~ m2_relset_1(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X4,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X4)
| ~ m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X5)
| k1_realset1(X3,X1) != X5
| k1_realset1(X2,X1) != X4
| ~ r4_binop_1(X0,X2,X3)
| r4_binop_1(X1,X4,X5) ),
inference(cnf_transformation,[],[f72]) ).
fof(f161,plain,
! [X2,X3,X0,X1,X5] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ~ m2_relset_1(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(k1_realset1(X2,X1))
| ~ m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X5)
| k1_realset1(X3,X1) != X5
| ~ r4_binop_1(X0,X2,X3)
| r4_binop_1(X1,k1_realset1(X2,X1),X5) ),
inference(equality_resolution,[],[f154]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ~ m2_relset_1(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(k1_realset1(X2,X1))
| ~ m2_relset_1(k1_realset1(X3,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X3,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(k1_realset1(X3,X1))
| ~ r4_binop_1(X0,X2,X3)
| r4_binop_1(X1,k1_realset1(X2,X1),k1_realset1(X3,X1)) ),
inference(equality_resolution,[],[f161]) ).
fof(f163,plain,
! [X2,X3,X0,X1,X5] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ~ m2_relset_1(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(k1_realset1(X2,X1))
| ~ m2_relset_1(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X5,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(X5)
| k1_realset1(X3,X1) != X5
| ~ r5_binop_1(X0,X2,X3)
| r5_binop_1(X1,k1_realset1(X2,X1),X5) ),
inference(equality_resolution,[],[f153]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X1)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X2)
| ~ m2_relset_1(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X3,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_1(X3)
| ~ m2_relset_1(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(k1_realset1(X2,X1))
| ~ m2_relset_1(k1_realset1(X3,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X3,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_1(k1_realset1(X3,X1))
| ~ r5_binop_1(X0,X2,X3)
| r5_binop_1(X1,k1_realset1(X2,X1),k1_realset1(X3,X1)) ),
inference(equality_resolution,[],[f163]) ).
tcf(c_49,negated_conjecture,
~ r6_binop_1(sK1,sK4,sK5),
inference(cnf_transformation,[],[f112]) ).
tcf(c_50,negated_conjecture,
k1_realset1(sK2,sK1) = sK4,
inference(cnf_transformation,[],[f111]) ).
tcf(c_51,negated_conjecture,
k1_realset1(sK3,sK1) = sK5,
inference(cnf_transformation,[],[f110]) ).
tcf(c_52,negated_conjecture,
r6_binop_1(sK0,sK2,sK3),
inference(cnf_transformation,[],[f109]) ).
tcf(c_53,negated_conjecture,
v1_funct_1(sK5),
inference(cnf_transformation,[],[f108]) ).
tcf(c_54,negated_conjecture,
v1_funct_2(sK5,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f107]) ).
tcf(c_55,negated_conjecture,
m2_relset_1(sK5,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f106]) ).
tcf(c_56,negated_conjecture,
v1_funct_1(sK4),
inference(cnf_transformation,[],[f105]) ).
tcf(c_57,negated_conjecture,
v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f104]) ).
tcf(c_58,negated_conjecture,
m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1),
inference(cnf_transformation,[],[f103]) ).
tcf(c_59,negated_conjecture,
v1_funct_1(sK3),
inference(cnf_transformation,[],[f102]) ).
tcf(c_60,negated_conjecture,
v1_funct_2(sK3,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f101]) ).
tcf(c_61,negated_conjecture,
m2_relset_1(sK3,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f100]) ).
tcf(c_62,negated_conjecture,
v1_funct_1(sK2),
inference(cnf_transformation,[],[f99]) ).
tcf(c_63,negated_conjecture,
v1_funct_2(sK2,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f98]) ).
tcf(c_64,negated_conjecture,
m2_relset_1(sK2,k2_zfmisc_1(sK0,sK0),sK0),
inference(cnf_transformation,[],[f97]) ).
tcf(c_65,negated_conjecture,
~ v1_xboole_0(sK1),
inference(cnf_transformation,[],[f96]) ).
tcf(c_66,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f95]) ).
tcf(c_67,negated_conjecture,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f94]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( r6_binop_1(X1,X0,X2)
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X0)
| ~ r5_binop_1(X1,X0,X2)
| ~ r4_binop_1(X1,X0,X2)
| ~ m2_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( r4_binop_1(X1,X0,X2)
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X0)
| ~ r6_binop_1(X1,X0,X2)
| ~ m2_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( r5_binop_1(X1,X0,X2)
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X0)
| ~ r6_binop_1(X1,X0,X2)
| ~ m2_relset_1(X2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X3)
| v1_xboole_0(X1)
| r4_binop_1(X1,k1_realset1(X0,X1),k1_realset1(X2,X1))
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| ~ v1_funct_1(k1_realset1(X2,X1))
| ~ v1_funct_1(k1_realset1(X0,X1))
| ~ r4_binop_1(X3,X0,X2)
| ~ m2_relset_1(X2,k2_zfmisc_1(X3,X3),X3)
| ~ m2_relset_1(X0,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_2(X2,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_2(X0,k2_zfmisc_1(X3,X3),X3)
| ~ m2_relset_1(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(k1_realset1(X0,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X0,X1),k2_zfmisc_1(X1,X1),X1) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X3)
| v1_xboole_0(X1)
| r5_binop_1(X1,k1_realset1(X0,X1),k1_realset1(X2,X1))
| ~ v1_funct_1(X2)
| ~ v1_funct_1(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| ~ v1_funct_1(k1_realset1(X2,X1))
| ~ v1_funct_1(k1_realset1(X0,X1))
| ~ r5_binop_1(X3,X0,X2)
| ~ m2_relset_1(X2,k2_zfmisc_1(X3,X3),X3)
| ~ m2_relset_1(X0,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_2(X2,k2_zfmisc_1(X3,X3),X3)
| ~ v1_funct_2(X0,k2_zfmisc_1(X3,X3),X3)
| ~ m2_relset_1(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(k1_realset1(X0,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X2,X1),k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(k1_realset1(X0,X1),k2_zfmisc_1(X1,X1),X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_funct_1(X2)
| ~ v1_funct_1(X1)
| ~ r5_binop_1(X0,X1,X2)
| ~ r4_binop_1(X0,X1,X2)
| ~ m2_relset_1(X2,k2_zfmisc_1(X0,X0),X0)
| ~ m2_relset_1(X1,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X2,k2_zfmisc_1(X0,X0),X0)
| ~ v1_funct_2(X1,k2_zfmisc_1(X0,X0),X0)
| ( X2 != sK5 )
| ( X1 != sK4 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_71]) ).
tcf(c_877,plain,
( ~ v1_funct_1(sK5)
| ~ v1_funct_1(sK4)
| ~ r5_binop_1(sK1,sK4,sK5)
| ~ r4_binop_1(sK1,sK4,sK5)
| ~ m2_relset_1(sK5,k2_zfmisc_1(sK1,sK1),sK1)
| ~ m2_relset_1(sK4,k2_zfmisc_1(sK1,sK1),sK1)
| ~ v1_funct_2(sK5,k2_zfmisc_1(sK1,sK1),sK1)
| ~ v1_funct_2(sK4,k2_zfmisc_1(sK1,sK1),sK1) ),
inference(unflattening,[status(thm)],[c_876]) ).
tcf(c_878,plain,
( ~ r5_binop_1(sK1,sK4,sK5)
| ~ r4_binop_1(sK1,sK4,sK5) ),
inference(global_subsumption_just,[status(thm)],[c_877,c_56,c_53,c_58,c_57,c_55,c_54,c_877]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i,X2: $i] :
( r5_binop_1(X2,X0,X1)
| ~ v1_funct_1(X1)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X1,k2_zfmisc_1(X2,X2),X2)
| ~ m2_relset_1(X0,k2_zfmisc_1(X2,X2),X2)
| ~ v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)
| ~ v1_funct_2(X0,k2_zfmisc_1(X2,X2),X2)
| ( X2 != sK0 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_73]) ).
tcf(c_887,plain,
( r5_binop_1(sK0,sK2,sK3)
| ~ v1_funct_1(sK3)
| ~ v1_funct_1(sK2)
| ~ m2_relset_1(sK3,k2_zfmisc_1(sK0,sK0),sK0)
| ~ m2_relset_1(sK2,k2_zfmisc_1(sK0,sK0),sK0)
| ~ v1_funct_2(sK3,k2_zfmisc_1(sK0,sK0),sK0)
| ~ v1_funct_2(sK2,k2_zfmisc_1(sK0,sK0),sK0) ),
inference(unflattening,[status(thm)],[c_886]) ).
tcf(c_888,plain,
r5_binop_1(sK0,sK2,sK3),
inference(global_subsumption_just,[status(thm)],[c_887,c_62,c_59,c_64,c_63,c_61,c_60,c_887]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i,X2: $i] :
( r4_binop_1(X2,X0,X1)
| ~ v1_funct_1(X1)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(X1,k2_zfmisc_1(X2,X2),X2)
| ~ m2_relset_1(X0,k2_zfmisc_1(X2,X2),X2)
| ~ v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)
| ~ v1_funct_2(X0,k2_zfmisc_1(X2,X2),X2)
| ( X2 != sK0 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_72]) ).
tcf(c_894,plain,
( r4_binop_1(sK0,sK2,sK3)
| ~ v1_funct_1(sK3)
| ~ v1_funct_1(sK2)
| ~ m2_relset_1(sK3,k2_zfmisc_1(sK0,sK0),sK0)
| ~ m2_relset_1(sK2,k2_zfmisc_1(sK0,sK0),sK0)
| ~ v1_funct_2(sK3,k2_zfmisc_1(sK0,sK0),sK0)
| ~ v1_funct_2(sK2,k2_zfmisc_1(sK0,sK0),sK0) ),
inference(unflattening,[status(thm)],[c_893]) ).
tcf(c_895,plain,
r4_binop_1(sK0,sK2,sK3),
inference(global_subsumption_just,[status(thm)],[c_894,c_62,c_59,c_64,c_63,c_61,c_60,c_894]) ).
tcf(c_1330,definition,
iPr_def_10 = k1_zfmisc_1(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1331,definition,
iPr_def_11 = k2_zfmisc_1(sK0,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1332,definition,
iPr_def_12 = k2_zfmisc_1(sK1,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1333,definition,
iPr_def_13 = k1_realset1(sK3,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1334,definition,
iPr_def_14 = k1_realset1(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1335,plain,
r4_binop_1(sK0,sK2,sK3),
inference(demodulation,[status(thm)],[c_895]) ).
tcf(c_1336,plain,
r5_binop_1(sK0,sK2,sK3),
inference(demodulation,[status(thm)],[c_888]) ).
tcf(c_1337,plain,
( ~ r5_binop_1(sK1,sK4,sK5)
| ~ r4_binop_1(sK1,sK4,sK5) ),
inference(demodulation,[status(thm)],[c_878]) ).
tcf(c_1339,negated_conjecture,
~ v1_xboole_0(sK0),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_1340,negated_conjecture,
m1_subset_1(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_66,c_1330]) ).
tcf(c_1341,negated_conjecture,
~ v1_xboole_0(sK1),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_1342,negated_conjecture,
m2_relset_1(sK2,iPr_def_11,sK0),
inference(demodulation,[status(thm)],[c_64,c_1331]) ).
tcf(c_1343,negated_conjecture,
v1_funct_2(sK2,iPr_def_11,sK0),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_1344,negated_conjecture,
v1_funct_1(sK2),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_1345,negated_conjecture,
m2_relset_1(sK3,iPr_def_11,sK0),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_1346,negated_conjecture,
v1_funct_2(sK3,iPr_def_11,sK0),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_1347,negated_conjecture,
v1_funct_1(sK3),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_1348,negated_conjecture,
m2_relset_1(sK4,iPr_def_12,sK1),
inference(demodulation,[status(thm)],[c_58,c_1332]) ).
tcf(c_1349,negated_conjecture,
v1_funct_2(sK4,iPr_def_12,sK1),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_1350,negated_conjecture,
v1_funct_1(sK4),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_1351,negated_conjecture,
m2_relset_1(sK5,iPr_def_12,sK1),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_1352,negated_conjecture,
v1_funct_2(sK5,iPr_def_12,sK1),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_1353,negated_conjecture,
v1_funct_1(sK5),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_1354,negated_conjecture,
iPr_def_13 = sK5,
inference(demodulation,[status(thm)],[c_51,c_1333]) ).
tcf(c_1355,negated_conjecture,
iPr_def_14 = sK4,
inference(demodulation,[status(thm)],[c_50,c_1334]) ).
tcf(c_2071,plain,
v1_funct_1(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_1350,c_1355]) ).
tcf(c_2072,plain,
v1_funct_1(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_1353,c_1354]) ).
tcf(c_2073,plain,
m2_relset_1(iPr_def_14,iPr_def_12,sK1),
inference(light_normalisation,[status(thm)],[c_1348,c_1355]) ).
tcf(c_2074,plain,
v1_funct_2(iPr_def_14,iPr_def_12,sK1),
inference(light_normalisation,[status(thm)],[c_1349,c_1355]) ).
tcf(c_2075,plain,
m2_relset_1(iPr_def_13,iPr_def_12,sK1),
inference(light_normalisation,[status(thm)],[c_1351,c_1354]) ).
tcf(c_2076,plain,
v1_funct_2(iPr_def_13,iPr_def_12,sK1),
inference(light_normalisation,[status(thm)],[c_1352,c_1354]) ).
tcf(c_2079,plain,
( ~ r5_binop_1(sK1,iPr_def_14,iPr_def_13)
| ~ r4_binop_1(sK1,iPr_def_14,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_1337,c_1354,c_1355]) ).
tcf(c_2514,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| v1_xboole_0(X1)
| r4_binop_1(sK1,k1_realset1(sK2,sK1),k1_realset1(X0,sK1))
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(X0)
| ~ v1_funct_1(k1_realset1(sK2,sK1))
| ~ m1_subset_1(sK1,k1_zfmisc_1(X1))
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ r4_binop_1(X1,sK2,X0)
| ~ v1_funct_2(iPr_def_14,k2_zfmisc_1(sK1,sK1),sK1)
| ~ m2_relset_1(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(k1_realset1(sK2,sK1),k2_zfmisc_1(sK1,sK1),sK1)
| ~ m2_relset_1(k1_realset1(X0,sK1),k2_zfmisc_1(sK1,sK1),sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),k2_zfmisc_1(sK1,sK1),sK1) ),
inference(superposition,[status(thm)],[c_1334,c_106]) ).
tcf(c_2568,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| v1_xboole_0(X1)
| r4_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(iPr_def_14)
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(iPr_def_14,iPr_def_12,sK1)
| ~ v1_funct_2(iPr_def_14,iPr_def_12,sK1)
| ~ m1_subset_1(sK1,k1_zfmisc_1(X1))
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ r4_binop_1(X1,sK2,X0)
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ m2_relset_1(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1) ),
inference(light_normalisation,[status(thm)],[c_2514,c_1332,c_1334]) ).
tcf(c_2569,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r4_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(X1))
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ r4_binop_1(X1,sK2,X0)
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ m2_relset_1(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2568,c_1341,c_2071,c_1344,c_2073,c_2074]) ).
tcf(c_2623,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| v1_xboole_0(X1)
| r5_binop_1(sK1,k1_realset1(sK2,sK1),k1_realset1(X0,sK1))
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(X0)
| ~ v1_funct_1(k1_realset1(sK2,sK1))
| ~ m1_subset_1(sK1,k1_zfmisc_1(X1))
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ r5_binop_1(X1,sK2,X0)
| ~ v1_funct_2(iPr_def_14,k2_zfmisc_1(sK1,sK1),sK1)
| ~ m2_relset_1(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(k1_realset1(sK2,sK1),k2_zfmisc_1(sK1,sK1),sK1)
| ~ m2_relset_1(k1_realset1(X0,sK1),k2_zfmisc_1(sK1,sK1),sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),k2_zfmisc_1(sK1,sK1),sK1) ),
inference(superposition,[status(thm)],[c_1334,c_107]) ).
tcf(c_2677,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK1)
| v1_xboole_0(X1)
| r5_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(iPr_def_14)
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(X0)
| ~ m2_relset_1(iPr_def_14,iPr_def_12,sK1)
| ~ v1_funct_2(iPr_def_14,iPr_def_12,sK1)
| ~ m1_subset_1(sK1,k1_zfmisc_1(X1))
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ r5_binop_1(X1,sK2,X0)
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ m2_relset_1(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1) ),
inference(light_normalisation,[status(thm)],[c_2623,c_1332,c_1334]) ).
tcf(c_2678,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r5_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(X1))
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ r5_binop_1(X1,sK2,X0)
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ m2_relset_1(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(sK2,k2_zfmisc_1(X1,X1),X1)
| ~ m2_relset_1(X0,k2_zfmisc_1(X1,X1),X1)
| ~ v1_funct_2(X0,k2_zfmisc_1(X1,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2677,c_1341,c_2071,c_1344,c_2073,c_2074]) ).
tcf(c_2975,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r4_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(sK0))
| ~ r4_binop_1(sK0,sK2,X0)
| ~ v1_funct_2(X0,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ m2_relset_1(sK2,k2_zfmisc_1(sK0,sK0),sK0)
| ~ v1_funct_2(sK2,k2_zfmisc_1(sK0,sK0),sK0)
| ~ m2_relset_1(X0,k2_zfmisc_1(sK0,sK0),sK0)
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1) ),
inference(superposition,[status(thm)],[c_1331,c_2569]) ).
tcf(c_2976,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r4_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ m1_subset_1(sK1,iPr_def_10)
| ~ m2_relset_1(sK2,iPr_def_11,sK0)
| ~ v1_funct_2(sK2,iPr_def_11,sK0)
| ~ r4_binop_1(sK0,sK2,X0)
| ~ m2_relset_1(X0,iPr_def_11,sK0)
| ~ v1_funct_2(X0,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1) ),
inference(light_normalisation,[status(thm)],[c_2975,c_1330,c_1331]) ).
tcf(c_2977,plain,
! [X0: $i] :
( r4_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ r4_binop_1(sK0,sK2,X0)
| ~ m2_relset_1(X0,iPr_def_11,sK0)
| ~ v1_funct_2(X0,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2976,c_1339,c_1340,c_1342,c_1343]) ).
tcf(c_3017,plain,
( r4_binop_1(sK1,iPr_def_14,k1_realset1(sK3,sK1))
| ~ v1_funct_1(sK3)
| ~ r4_binop_1(sK0,sK2,sK3)
| ~ m2_relset_1(sK3,iPr_def_11,sK0)
| ~ v1_funct_2(iPr_def_13,iPr_def_12,sK1)
| ~ v1_funct_2(sK3,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(sK3,sK1))
| ~ m2_relset_1(k1_realset1(sK3,sK1),iPr_def_12,sK1) ),
inference(superposition,[status(thm)],[c_1333,c_2977]) ).
tcf(c_3018,plain,
( r4_binop_1(sK1,iPr_def_14,iPr_def_13)
| ~ v1_funct_1(iPr_def_13)
| ~ v1_funct_1(sK3)
| ~ r4_binop_1(sK0,sK2,sK3)
| ~ m2_relset_1(iPr_def_13,iPr_def_12,sK1)
| ~ m2_relset_1(sK3,iPr_def_11,sK0)
| ~ v1_funct_2(iPr_def_13,iPr_def_12,sK1)
| ~ v1_funct_2(sK3,iPr_def_11,sK0) ),
inference(light_normalisation,[status(thm)],[c_3017,c_1333]) ).
tcf(c_3019,plain,
r4_binop_1(sK1,iPr_def_14,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_3018,c_2072,c_1347,c_1335,c_2075,c_1345,c_2076,c_1346]) ).
tcf(c_3024,plain,
~ r5_binop_1(sK1,iPr_def_14,iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_2079,c_3019]) ).
tcf(c_3258,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r5_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(sK0))
| ~ r5_binop_1(sK0,sK2,X0)
| ~ v1_funct_2(X0,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ m2_relset_1(sK2,k2_zfmisc_1(sK0,sK0),sK0)
| ~ v1_funct_2(sK2,k2_zfmisc_1(sK0,sK0),sK0)
| ~ m2_relset_1(X0,k2_zfmisc_1(sK0,sK0),sK0)
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1) ),
inference(superposition,[status(thm)],[c_1331,c_2678]) ).
tcf(c_3259,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r5_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ m1_subset_1(sK1,iPr_def_10)
| ~ m2_relset_1(sK2,iPr_def_11,sK0)
| ~ v1_funct_2(sK2,iPr_def_11,sK0)
| ~ r5_binop_1(sK0,sK2,X0)
| ~ m2_relset_1(X0,iPr_def_11,sK0)
| ~ v1_funct_2(X0,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1) ),
inference(light_normalisation,[status(thm)],[c_3258,c_1330,c_1331]) ).
tcf(c_3260,plain,
! [X0: $i] :
( r5_binop_1(sK1,iPr_def_14,k1_realset1(X0,sK1))
| ~ v1_funct_1(X0)
| ~ r5_binop_1(sK0,sK2,X0)
| ~ m2_relset_1(X0,iPr_def_11,sK0)
| ~ v1_funct_2(X0,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(X0,sK1))
| ~ m2_relset_1(k1_realset1(X0,sK1),iPr_def_12,sK1)
| ~ v1_funct_2(k1_realset1(X0,sK1),iPr_def_12,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3259,c_1339,c_1340,c_1342,c_1343]) ).
tcf(c_3300,plain,
( r5_binop_1(sK1,iPr_def_14,k1_realset1(sK3,sK1))
| ~ v1_funct_1(sK3)
| ~ r5_binop_1(sK0,sK2,sK3)
| ~ m2_relset_1(sK3,iPr_def_11,sK0)
| ~ v1_funct_2(iPr_def_13,iPr_def_12,sK1)
| ~ v1_funct_2(sK3,iPr_def_11,sK0)
| ~ v1_funct_1(k1_realset1(sK3,sK1))
| ~ m2_relset_1(k1_realset1(sK3,sK1),iPr_def_12,sK1) ),
inference(superposition,[status(thm)],[c_1333,c_3260]) ).
tcf(c_3301,plain,
( r5_binop_1(sK1,iPr_def_14,iPr_def_13)
| ~ v1_funct_1(iPr_def_13)
| ~ v1_funct_1(sK3)
| ~ r5_binop_1(sK0,sK2,sK3)
| ~ m2_relset_1(iPr_def_13,iPr_def_12,sK1)
| ~ m2_relset_1(sK3,iPr_def_11,sK0)
| ~ v1_funct_2(iPr_def_13,iPr_def_12,sK1)
| ~ v1_funct_2(sK3,iPr_def_11,sK0) ),
inference(light_normalisation,[status(thm)],[c_3300,c_1333]) ).
tcf(c_3302,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3301,c_3024,c_2072,c_1347,c_1336,c_2075,c_1345,c_2076,c_1346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT294+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 20:53:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 3.49/1.28 % SZS status Started for theBenchmark.p
% 3.49/1.28 % SZS status Theorem for theBenchmark.p
% 3.49/1.28
% 3.49/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.49/1.28
% 3.49/1.28 % ------ iProver source info
% 3.49/1.28
% 3.49/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.49/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.49/1.28 % git: non_committed_changes: false
% 3.49/1.28
% 3.49/1.28 % ------ Parsing...
% 3.49/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.49/1.28
% 3.49/1.28 % ------ 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 %
% 3.49/1.28
% 3.49/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.49/1.28
% 3.49/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.49/1.28 % ------ Proving...
% 3.49/1.28 % ------ Problem Properties
% 3.49/1.28
% 3.49/1.28 %
% 3.49/1.28 % clauses 65
% 3.49/1.28 % conjectures 17
% 3.49/1.28 % EPR 38
% 3.49/1.28 % Horn 60
% 3.49/1.28 % unary 42
% 3.49/1.28 % binary 13
% 3.49/1.28 % lits 126
% 3.49/1.28 % lits eq 13
% 3.49/1.28 % fd_pure 0
% 3.49/1.28 % fd_pseudo 0
% 3.49/1.28 % fd_cond 1
% 3.49/1.28 % fd_pseudo_cond 1
% 3.49/1.28 % AC symbols 0
% 3.49/1.28
% 3.49/1.28 % ------ Schedule dynamic 5 is on
% 3.49/1.28
% 3.49/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.49/1.28
% 3.49/1.28
% 3.49/1.28 % ------
% 3.49/1.28 % Current options:
% 3.49/1.28 % ------
% 3.49/1.28
% 3.49/1.28
% 3.49/1.28 %
% 3.49/1.28
% 3.49/1.28 % ------ Proving...
% 3.49/1.28 %
% 3.49/1.28
% 3.49/1.28 % SZS status Theorem for theBenchmark.p
% 3.49/1.28
% 3.49/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.49/1.28
% 3.49/1.28
%------------------------------------------------------------------------------