%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU439+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 : n012.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 02:57:32 PM UTC 2026
% Result : Theorem 5.96s 2.16s
% Output : CNFRefutation 5.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 98 ( 22 unt; 0 def)
% Number of atoms : 307 ( 36 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 368 ( 159 ~; 145 |; 40 &)
% ( 10 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 241 ( 0 sgn 221 !; 20 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( X2 != k1_xboole_0
=> r1_tarski(k8_relset_2(X0,X1,X2,X3),k9_relat_1(X3,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( X2 != k1_xboole_0
=> r1_tarski(k8_relset_2(X0,X1,X2,X3),k9_relat_1(X3,X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f7,axiom,
! [X0] :
( v1_relat_1(X0)
=> ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f8,axiom,
! [X0] :
( X0 = k1_xboole_0
<=> ! [X1] : ~ r2_hidden(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f9,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f11,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f39,axiom,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f53,axiom,
! [X0,X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X0))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( r2_hidden(X2,k8_relset_2(X0,X1,X3,X4))
=> ! [X5] :
( r2_hidden(X5,X3)
=> r2_hidden(X2,k9_relat_1(X4,k1_tarski(X5))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relset_2) ).
fof(f55,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f57,axiom,
! [X0,X1,X2] :
~ ( v1_xboole_0(X2)
& m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f61,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
<=> r2_hidden(k4_tarski(X1,X0),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_2) ).
fof(f69,plain,
? [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& X2 != k1_xboole_0
& ~ r1_tarski(k8_relset_2(X0,X1,X2,X3),k9_relat_1(X3,X2)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f70,plain,
? [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
& ? [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& X2 != k1_xboole_0
& ~ r1_tarski(k8_relset_2(X0,X1,X2,X3),k9_relat_1(X3,X2)) ) ),
inference(flattening,[],[f69]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f74,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( X2 = k9_relat_1(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f75,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X0))
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ r2_hidden(X2,k8_relset_2(X0,X1,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| r2_hidden(X2,k9_relat_1(X4,k1_tarski(X5))) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X0))
| ! [X4] :
( ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ r2_hidden(X2,k8_relset_2(X0,X1,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| r2_hidden(X2,k9_relat_1(X4,k1_tarski(X5))) ) ) ),
inference(flattening,[],[f93]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ( r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
<=> r2_hidden(k4_tarski(X1,X0),X2) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f104,plain,
( m1_subset_1(sK2,k1_zfmisc_1(sK0))
& m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
& k1_xboole_0 != sK2
& ~ r1_tarski(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f70]) ).
fof(f105,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( k9_relat_1(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) )
& ( ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,X3),X0) )
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ? [X4] :
( r2_hidden(X4,X1)
& r2_hidden(k4_tarski(X4,X3),X0) ) )
& ( ~ r2_hidden(X3,X2)
| ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,X3),X0) ) ) )
| X2 = k9_relat_1(X0,X1) ) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f106,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( k9_relat_1(X0,X1) != X2
| ! [X6] :
( ( ~ r2_hidden(X6,X2)
| ? [X8] :
( r2_hidden(X8,X1)
& r2_hidden(k4_tarski(X8,X6),X0) ) )
& ( ! [X7] :
( ~ r2_hidden(X7,X1)
| ~ r2_hidden(k4_tarski(X7,X6),X0) )
| r2_hidden(X6,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ? [X5] :
( r2_hidden(X5,X1)
& r2_hidden(k4_tarski(X5,X3),X0) ) )
& ( ~ r2_hidden(X3,X2)
| ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,X3),X0) ) ) )
| X2 = k9_relat_1(X0,X1) ) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( k9_relat_1(X0,X1) != X2
| ! [X6] :
( ( ~ r2_hidden(X6,X2)
| ( r2_hidden(sK6(X0,X1,X6),X1)
& r2_hidden(k4_tarski(sK6(X0,X1,X6),X6),X0) ) )
& ( ! [X7] :
( ~ r2_hidden(X7,X1)
| ~ r2_hidden(k4_tarski(X7,X6),X0) )
| r2_hidden(X6,X2) ) ) )
& ( ( ( r2_hidden(sK4(X0,X1,X2),X2)
| ( r2_hidden(sK5(X0,X1,X2),X1)
& r2_hidden(k4_tarski(sK5(X0,X1,X2),sK4(X0,X1,X2)),X0) ) )
& ( ~ r2_hidden(sK4(X0,X1,X2),X2)
| ! [X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(k4_tarski(X4,sK4(X0,X1,X2)),X0) ) ) )
| X2 = k9_relat_1(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X5,sK5(X0,X1,X2)),skolemize(X8,sK6(X0,X1,X6))],[f106]) ).
fof(f108,plain,
! [X0] :
( ( k1_xboole_0 != X0
| ! [X1] : ~ r2_hidden(X1,X0) )
& ( ? [X1] : r2_hidden(X1,X0)
| X0 = k1_xboole_0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f109,plain,
! [X0] :
( ( k1_xboole_0 != X0
| ! [X2] : ~ r2_hidden(X2,X0) )
& ( ? [X1] : r2_hidden(X1,X0)
| X0 = k1_xboole_0 ) ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ( k1_xboole_0 != X0
| ! [X2] : ~ r2_hidden(X2,X0) )
& ( r2_hidden(sK7(X0),X0)
| X0 = k1_xboole_0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f112,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(rectify,[],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ( r2_hidden(sK8(X0,X1),X0)
& ~ r2_hidden(sK8(X0,X1),X1) )
| r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f112]) ).
fof(f125,plain,
! [X0,X1] :
( ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) )
& ( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ v1_relat_1(X2)
| ( ( ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k4_tarski(X1,X0),X2) )
& ( ~ r2_hidden(k4_tarski(X1,X0),X2)
| r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1))) ) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f127,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f104]) ).
fof(f128,plain,
m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f104]) ).
fof(f129,plain,
k1_xboole_0 != sK2,
inference(cnf_transformation,[],[f104]) ).
fof(f130,plain,
~ r1_tarski(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),
inference(cnf_transformation,[],[f104]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f134,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f137,plain,
! [X2,X0,X1,X6,X7] :
( ~ v1_relat_1(X0)
| k9_relat_1(X0,X1) != X2
| ~ r2_hidden(X7,X1)
| ~ r2_hidden(k4_tarski(X7,X6),X0)
| r2_hidden(X6,X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f142,plain,
! [X0] :
( r2_hidden(sK7(X0),X0)
| k1_xboole_0 = X0 ),
inference(cnf_transformation,[],[f110]) ).
fof(f143,plain,
! [X3,X0,X1] :
( ~ r1_tarski(X0,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f144,plain,
! [X0,X1] :
( r2_hidden(sK8(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f145,plain,
! [X0,X1] :
( ~ r2_hidden(sK8(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f147,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f167,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f39]) ).
fof(f187,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ m1_subset_1(X3,k1_zfmisc_1(X0))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ r2_hidden(X2,k8_relset_2(X0,X1,X3,X4))
| ~ r2_hidden(X5,X3)
| r2_hidden(X2,k9_relat_1(X4,k1_tarski(X5))) ),
inference(cnf_transformation,[],[f94]) ).
fof(f189,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f190,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k4_tarski(X1,X0),X2) ),
inference(cnf_transformation,[],[f126]) ).
fof(f200,plain,
! [X2,X0,X1,X6,X7] :
( ~ v1_relat_1(X0)
| k9_relat_1(X0,X1) != X2
| ~ r2_hidden(X7,X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| r2_hidden(X6,X2) ),
inference(definition_unfolding,[],[f137,f147]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| ~ r2_hidden(X0,k9_relat_1(X2,k1_tarski(X1)))
| r2_hidden(k2_tarski(k2_tarski(X1,X0),k1_tarski(X1)),X2) ),
inference(definition_unfolding,[],[f196,f147]) ).
fof(f204,plain,
! [X0,X1,X6,X7] :
( ~ v1_relat_1(X0)
| ~ r2_hidden(X7,X1)
| ~ r2_hidden(k2_tarski(k2_tarski(X7,X6),k1_tarski(X7)),X0)
| r2_hidden(X6,k9_relat_1(X0,X1)) ),
inference(equality_resolution,[],[f200]) ).
tcf(c_49,negated_conjecture,
~ r1_tarski(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),
inference(cnf_transformation,[],[f130]) ).
tcf(c_50,negated_conjecture,
sK2 != k1_xboole_0,
inference(cnf_transformation,[],[f129]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f128]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f127]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_relat_1(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f134]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X1,k9_relat_1(X2,X3))
| ~ v1_relat_1(X2)
| ~ r2_hidden(X0,X3)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),X2) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_63,plain,
! [X0: $i] :
( r2_hidden(sK7(X0),X0)
| ( X0 = k1_xboole_0 ) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_87,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f167]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r2_hidden(X0,k9_relat_1(X4,k1_tarski(X5)))
| ~ r2_hidden(X5,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ r2_hidden(X0,k8_relset_2(X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k2_tarski(k2_tarski(X2,X0),k1_tarski(X2)),X1)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2))) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK8(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK8(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK8(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_201]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,X0)
| ~ r1_tarski(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_113,c_163]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(k2_tarski(k1_tarski(X2),k2_tarski(X2,X0)),X1)
| ~ v1_relat_1(X1)
| ~ r2_hidden(X0,k9_relat_1(X1,k1_tarski(X2))) ),
inference(demodulation,[status(thm)],[c_118,c_56]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X1,k9_relat_1(X2,X3))
| ~ v1_relat_1(X2)
| ~ r2_hidden(X0,X3)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[c_60,c_56]) ).
tcf(c_822,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK8(X0,X1),X0)
| ( k9_relat_1(sK3,sK2) != X1 )
| ( k8_relset_2(sK0,sK1,sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_202]) ).
tcf(c_823,plain,
r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k8_relset_2(sK0,sK1,sK2,sK3)),
inference(unflattening,[status(thm)],[c_822]) ).
tcf(c_827,plain,
! [X0: $i,X1: $i] :
( ~ r2_hidden(sK8(X0,X1),X1)
| ( k9_relat_1(sK3,sK2) != X1 )
| ( k8_relset_2(sK0,sK1,sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_197]) ).
tcf(c_828,plain,
~ r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k9_relat_1(sK3,sK2)),
inference(unflattening,[status(thm)],[c_827]) ).
tcf(c_2598,plain,
( r2_hidden(sK7(sK2),sK2)
| ( sK2 = k1_xboole_0 ) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2603,plain,
! [X0: $i] :
( r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k9_relat_1(sK3,sK2))
| ~ v1_relat_1(sK3)
| ~ r2_hidden(X0,sK2)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)))),sK3) ),
inference(instantiation,[status(thm)],[c_614]) ).
tcf(c_2635,plain,
! [X0: $i] :
( ~ v1_xboole_0(X0)
| ~ r1_tarski(sK2,X0)
| ~ r2_hidden(sK7(sK2),sK2) ),
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_2636,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ r1_tarski(sK2,k1_xboole_0)
| ~ r2_hidden(sK7(sK2),sK2) ),
inference(instantiation,[status(thm)],[c_2635]) ).
tcf(c_2725,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(sK3)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_3019,plain,
( v1_relat_1(sK3)
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_2725]) ).
tcf(c_4173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k9_relat_1(X3,k1_tarski(X4)))
| ~ r2_hidden(X4,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k8_relset_2(X0,X1,X2,X3)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_10258,plain,
! [X0: $i] :
( r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k9_relat_1(sK3,k1_tarski(X0)))
| ~ r2_hidden(X0,sK2)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m1_subset_1(sK3,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k8_relset_2(sK0,sK1,sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_4173]) ).
tcf(c_21449,plain,
! [X0: $i] :
( r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)))),sK3)
| ~ v1_relat_1(sK3)
| ~ r2_hidden(sK8(k8_relset_2(sK0,sK1,sK2,sK3),k9_relat_1(sK3,sK2)),k9_relat_1(sK3,k1_tarski(X0))) ),
inference(instantiation,[status(thm)],[c_612]) ).
tcf(c_22246,plain,
r1_tarski(sK2,sK0),
inference(superposition,[status(thm)],[c_52,c_111]) ).
tcf(c_22278,plain,
! [X0: $i] :
( r2_hidden(X0,sK0)
| ~ r2_hidden(X0,sK2) ),
inference(superposition,[status(thm)],[c_22246,c_67]) ).
tcf(c_22310,plain,
! [X0: $i] : ~ r2_hidden(X0,sK2),
inference(global_subsumption_just,[status(thm)],[c_22278,c_52,c_51,c_823,c_828,c_2603,c_3019,c_10258,c_21449]) ).
tcf(c_22314,plain,
! [X0: $i] : r1_tarski(sK2,X0),
inference(superposition,[status(thm)],[c_66,c_22310]) ).
tcf(c_22315,plain,
r1_tarski(sK2,k1_xboole_0),
inference(instantiation,[status(thm)],[c_22314]) ).
tcf(c_22316,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_22315,c_2636,c_2598,c_50,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU439+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 14:15:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 5.96/2.16 % SZS status Started for theBenchmark.p
% 5.96/2.16 % SZS status Theorem for theBenchmark.p
% 5.96/2.16
% 5.96/2.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.96/2.16
% 5.96/2.16 % ------ iProver source info
% 5.96/2.16
% 5.96/2.16 % git: date: 2026-07-19 20:42:38 +0200
% 5.96/2.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.96/2.16 % git: non_committed_changes: false
% 5.96/2.16
% 5.96/2.16 % ------ Parsing...
% 5.96/2.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.96/2.16
% 5.96/2.16 % ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 5.96/2.16
% 5.96/2.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.96/2.16
% 5.96/2.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 5.96/2.16 % ------ Proving...
% 5.96/2.16 % ------ Problem Properties
% 5.96/2.16
% 5.96/2.16 %
% 5.96/2.16 % clauses 64
% 5.96/2.16 % conjectures 4
% 5.96/2.16 % EPR 20
% 5.96/2.16 % Horn 57
% 5.96/2.16 % unary 27
% 5.96/2.16 % binary 19
% 5.96/2.16 % lits 126
% 5.96/2.16 % lits eq 12
% 5.96/2.16 % fd_pure 0
% 5.96/2.16 % fd_pseudo 0
% 5.96/2.16 % fd_cond 2
% 5.96/2.16 % fd_pseudo_cond 4
% 5.96/2.16 % AC symbols 0
% 5.96/2.16
% 5.96/2.16 % ------ Input Options Time Limit: Unbounded
% 5.96/2.16
% 5.96/2.16
% 5.96/2.16 % ------
% 5.96/2.16 % Current options:
% 5.96/2.16 % ------
% 5.96/2.16
% 5.96/2.16
% 5.96/2.16 %
% 5.96/2.16
% 5.96/2.16 % ------ Proving...
% 5.96/2.16 %
% 5.96/2.16
% 5.96/2.16 % SZS status Theorem for theBenchmark.p
% 5.96/2.16
% 5.96/2.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.96/2.16
% 5.96/2.16
%------------------------------------------------------------------------------