%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU424+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Tue Sep 29 12:48:55 PM UTC 2026
% Result : Theorem 10.19s 2.45s
% Output : Refutation 10.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 15 unt; 3 def)
% Number of atoms : 252 ( 16 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 275 ( 99 ~; 114 |; 37 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 146 ( 0 sgn 135 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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(f334,axiom,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f343,axiom,
! [X0,X1] :
( ( ~ v1_xboole_0(X0)
=> ( m1_subset_1(X1,X0)
<=> r2_hidden(X1,X0) ) )
& ( v1_xboole_0(X0)
=> ( m1_subset_1(X1,X0)
<=> v1_xboole_0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f540,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(f1181,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f4453,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ v1_xboole_0(X1)
& m1_subset_1(X3,k1_zfmisc_1(X1))
& m2_relset_1(X4,X1,X2) )
=> ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( m1_subset_1(X5,X1)
& X0 = k2_relset_2(X1,X2,X4,X5)
& r2_hidden(X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_0_relset_2) ).
fof(f4459,axiom,
! [X0,X1,X2,X3] :
( ( m1_relset_1(X2,X0,X1)
& m1_subset_1(X3,X0) )
=> m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relset_2) ).
fof(f4490,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relset_2) ).
fof(f4491,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f4490]) ).
fof(f4512,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( m1_subset_1(X5,X1)
& X0 = k2_relset_2(X1,X2,X4,X5)
& r2_hidden(X5,X3) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2) ),
inference(ennf_transformation,[],[f4453]) ).
fof(f4513,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( m1_subset_1(X5,X1)
& X0 = k2_relset_2(X1,X2,X4,X5)
& r2_hidden(X5,X3) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2) ),
inference(flattening,[],[f4512]) ).
fof(f4522,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1)
| ~ m1_subset_1(X3,X0) ),
inference(ennf_transformation,[],[f4459]) ).
fof(f4523,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1)
| ~ m1_subset_1(X3,X0) ),
inference(flattening,[],[f4522]) ).
fof(f4552,plain,
? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f4491]) ).
fof(f4565,plain,
! [X0,X1] :
( ( ( m1_subset_1(X1,X0)
<=> r2_hidden(X1,X0) )
| v1_xboole_0(X0) )
& ( ( m1_subset_1(X1,X0)
<=> v1_xboole_0(X1) )
| ~ v1_xboole_0(X0) ) ),
inference(ennf_transformation,[],[f343]) ).
fof(f4860,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f6192,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ m1_subset_1(X5,X1)
| k2_relset_2(X1,X2,X4,X5) != X0
| ~ r2_hidden(X5,X3) ) )
& ( ? [X5] :
( m1_subset_1(X5,X1)
& X0 = k2_relset_2(X1,X2,X4,X5)
& r2_hidden(X5,X3) )
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4)) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2) ),
inference(nnf_transformation,[],[f4513]) ).
fof(f6193,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ m1_subset_1(X5,X1)
| k2_relset_2(X1,X2,X4,X5) != X0
| ~ r2_hidden(X5,X3) ) )
& ( ? [X6] :
( m1_subset_1(X6,X1)
& k2_relset_2(X1,X2,X4,X6) = X0
& r2_hidden(X6,X3) )
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4)) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2) ),
inference(rectify,[],[f6192]) ).
fof(f6194,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ m1_subset_1(X5,X1)
| k2_relset_2(X1,X2,X4,X5) != X0
| ~ r2_hidden(X5,X3) ) )
& ( ( m1_subset_1(sK4(X0,X1,X2,X3,X4),X1)
& k2_relset_2(X1,X2,X4,sK4(X0,X1,X2,X3,X4)) = X0
& r2_hidden(sK4(X0,X1,X2,X3,X4),X3) )
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4)) ) )
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X6,sK4(X0,X1,X2,X3,X4))],[f6193]) ).
fof(f6201,plain,
( ~ m1_subset_1(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(k1_zfmisc_1(sK7)))
& m2_relset_1(sK9,sK6,sK7)
& m1_subset_1(sK8,k1_zfmisc_1(sK6))
& ~ v1_xboole_0(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f4552]) ).
fof(f6208,plain,
! [X0,X1] :
( ( ( ( m1_subset_1(X1,X0)
| ~ r2_hidden(X1,X0) )
& ( r2_hidden(X1,X0)
| ~ m1_subset_1(X1,X0) ) )
| v1_xboole_0(X0) )
& ( ( ( m1_subset_1(X1,X0)
| ~ v1_xboole_0(X1) )
& ( v1_xboole_0(X1)
| ~ m1_subset_1(X1,X0) ) )
| ~ v1_xboole_0(X0) ) ),
inference(nnf_transformation,[],[f4565]) ).
fof(f6214,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,[],[f540]) ).
fof(f6243,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1181]) ).
fof(f6305,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X2] :
( r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f4860]) ).
fof(f6306,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ? [X2] :
( ~ r2_hidden(X2,X1)
& r2_hidden(X2,X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(rectify,[],[f6305]) ).
fof(f6307,plain,
! [X0,X1] :
( ( r1_tarski(X0,X1)
| ( ~ r2_hidden(sK72(X0,X1),X1)
& r2_hidden(sK72(X0,X1),X0) ) )
& ( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) )
| ~ r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(X2,sK72(X0,X1))],[f6306]) ).
fof(f6741,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| k2_relset_2(X1,X2,X4,sK4(X0,X1,X2,X3,X4)) = X0
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2) ),
inference(cnf_transformation,[],[f6194]) ).
fof(f6742,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| m1_subset_1(sK4(X0,X1,X2,X3,X4),X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2) ),
inference(cnf_transformation,[],[f6194]) ).
fof(f6749,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1)
| ~ m1_subset_1(X3,X0) ),
inference(cnf_transformation,[],[f4523]) ).
fof(f6787,plain,
~ v1_xboole_0(sK6),
inference(cnf_transformation,[],[f6201]) ).
fof(f6788,plain,
m1_subset_1(sK8,k1_zfmisc_1(sK6)),
inference(cnf_transformation,[],[f6201]) ).
fof(f6789,plain,
m2_relset_1(sK9,sK6,sK7),
inference(cnf_transformation,[],[f6201]) ).
fof(f6790,plain,
~ m1_subset_1(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(k1_zfmisc_1(sK7))),
inference(cnf_transformation,[],[f6201]) ).
fof(f6813,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| r2_hidden(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f6208]) ).
fof(f6831,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f6214]) ).
fof(f6852,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f334]) ).
fof(f6931,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f6243]) ).
fof(f7267,plain,
! [X0,X1] :
( r2_hidden(sK72(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f6307]) ).
fof(f7268,plain,
! [X0,X1] :
( ~ r2_hidden(sK72(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f6307]) ).
fof(f11097,plain,
! [X2,X3,X0,X1,X4] :
( r1_tarski(a_4_0_relset_2(X0,X1,X2,X3),X4)
| sK72(a_4_0_relset_2(X0,X1,X2,X3),X4) = k2_relset_2(X0,X1,X3,sK4(sK72(a_4_0_relset_2(X0,X1,X2,X3),X4),X0,X1,X2,X3))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m2_relset_1(X3,X0,X1) ),
inference(resolution,[],[f7267,f6741]) ).
fof(f11098,plain,
! [X2,X3,X0,X1,X4] :
( ~ m2_relset_1(X3,X0,X1)
| m1_subset_1(sK4(sK72(a_4_0_relset_2(X0,X1,X2,X3),X4),X0,X1,X2,X3),X0)
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| r1_tarski(a_4_0_relset_2(X0,X1,X2,X3),X4) ),
inference(resolution,[],[f7267,f6742]) ).
fof(f11101,plain,
! [X2,X3,X0,X1,X4] :
( ~ m2_relset_1(X3,X0,X1)
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| sK72(a_4_0_relset_2(X0,X1,X2,X3),X4) = k2_relset_2(X0,X1,X3,sK4(sK72(a_4_0_relset_2(X0,X1,X2,X3),X4),X0,X1,X2,X3))
| m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X4)) ),
inference(resolution,[],[f11097,f6831]) ).
fof(f11102,plain,
! [X0,X1] :
( v1_xboole_0(sK6)
| ~ m1_subset_1(X0,k1_zfmisc_1(sK6))
| sK72(a_4_0_relset_2(sK6,sK7,X0,sK9),X1) = k2_relset_2(sK6,sK7,sK9,sK4(sK72(a_4_0_relset_2(sK6,sK7,X0,sK9),X1),sK6,sK7,X0,sK9))
| m1_subset_1(a_4_0_relset_2(sK6,sK7,X0,sK9),k1_zfmisc_1(X1)) ),
inference(resolution,[],[f11101,f6789]) ).
fof(f11103,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sK6))
| sK72(a_4_0_relset_2(sK6,sK7,X0,sK9),X1) = k2_relset_2(sK6,sK7,sK9,sK4(sK72(a_4_0_relset_2(sK6,sK7,X0,sK9),X1),sK6,sK7,X0,sK9))
| m1_subset_1(a_4_0_relset_2(sK6,sK7,X0,sK9),k1_zfmisc_1(X1)) ),
inference(forward_subsumption_resolution,[],[f11102,f6787]) ).
fof(f11112,plain,
! [X0,X1] :
( m1_subset_1(sK4(sK72(a_4_0_relset_2(sK6,sK7,X0,sK9),X1),sK6,sK7,X0,sK9),sK6)
| v1_xboole_0(sK6)
| ~ m1_subset_1(X0,k1_zfmisc_1(sK6))
| r1_tarski(a_4_0_relset_2(sK6,sK7,X0,sK9),X1) ),
inference(resolution,[],[f11098,f6789]) ).
fof(f11113,plain,
! [X0,X1] :
( m1_subset_1(sK4(sK72(a_4_0_relset_2(sK6,sK7,X0,sK9),X1),sK6,sK7,X0,sK9),sK6)
| ~ m1_subset_1(X0,k1_zfmisc_1(sK6))
| r1_tarski(a_4_0_relset_2(sK6,sK7,X0,sK9),X1) ),
inference(forward_subsumption_resolution,[],[f11112,f6787]) ).
fof(f11123,plain,
! [X0] :
( m1_subset_1(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(X0))
| sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),X0) = k2_relset_2(sK6,sK7,sK9,sK4(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),X0),sK6,sK7,sK8,sK9)) ),
inference(resolution,[],[f11103,f6788]) ).
fof(f11132,plain,
sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)) = k2_relset_2(sK6,sK7,sK9,sK4(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),sK6,sK7,sK8,sK9)),
inference(resolution,[],[f11123,f6790]) ).
fof(f11187,plain,
( m1_subset_1(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),k1_zfmisc_1(sK7))
| ~ m1_relset_1(sK9,sK6,sK7)
| ~ m1_subset_1(sK4(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),sK6,sK7,sK8,sK9),sK6) ),
inference(superposition,[],[f6749,f11132]) ).
fof(f11189,definition,
( spl342_46
<=> m1_subset_1(sK4(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),sK6,sK7,sK8,sK9),sK6) ),
introduced(definition,[new_symbols(definition,[spl342_46])],[avatar_definition]) ).
fof(f11190,plain,
( ~ m1_subset_1(sK4(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),sK6,sK7,sK8,sK9),sK6)
| spl342_46 ),
inference(avatar_component_clause,[],[f11189]) ).
fof(f11192,definition,
( spl342_47
<=> m1_relset_1(sK9,sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl342_47])],[avatar_definition]) ).
fof(f11193,plain,
( ~ m1_relset_1(sK9,sK6,sK7)
| spl342_47 ),
inference(avatar_component_clause,[],[f11192]) ).
fof(f11195,definition,
( spl342_48
<=> m1_subset_1(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),k1_zfmisc_1(sK7)) ),
introduced(definition,[new_symbols(definition,[spl342_48])],[avatar_definition]) ).
fof(f11196,plain,
( m1_subset_1(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),k1_zfmisc_1(sK7))
| ~ spl342_48 ),
inference(avatar_component_clause,[],[f11195]) ).
fof(f11197,plain,
( ~ spl342_46
| ~ spl342_47
| spl342_48 ),
inference(avatar_split_clause,[],[f11187,f11195,f11192,f11189]) ).
fof(f11198,plain,
( ~ m1_subset_1(sK8,k1_zfmisc_1(sK6))
| r1_tarski(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7))
| spl342_46 ),
inference(resolution,[],[f11190,f11113]) ).
fof(f11199,plain,
( r1_tarski(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7))
| spl342_46 ),
inference(forward_subsumption_resolution,[],[f11198,f6788]) ).
fof(f11201,plain,
( m1_subset_1(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(k1_zfmisc_1(sK7)))
| spl342_46 ),
inference(resolution,[],[f11199,f6831]) ).
fof(f11203,plain,
( $false
| spl342_46 ),
inference(forward_subsumption_resolution,[],[f11201,f6790]) ).
fof(f11204,plain,
spl342_46,
inference(avatar_contradiction_clause,[],[f11203]) ).
fof(f11206,plain,
( ~ m2_relset_1(sK9,sK6,sK7)
| spl342_47 ),
inference(resolution,[],[f11193,f6931]) ).
fof(f11208,plain,
( $false
| spl342_47 ),
inference(forward_subsumption_resolution,[],[f11206,f6789]) ).
fof(f11209,plain,
spl342_47,
inference(avatar_contradiction_clause,[],[f11208]) ).
fof(f11217,plain,
( r2_hidden(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),k1_zfmisc_1(sK7))
| v1_xboole_0(k1_zfmisc_1(sK7))
| ~ spl342_48 ),
inference(resolution,[],[f11196,f6813]) ).
fof(f11218,plain,
( r2_hidden(sK72(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7)),k1_zfmisc_1(sK7))
| ~ spl342_48 ),
inference(forward_subsumption_resolution,[],[f11217,f6852]) ).
fof(f11282,plain,
( r1_tarski(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(sK7))
| ~ spl342_48 ),
inference(resolution,[],[f11218,f7268]) ).
fof(f11554,plain,
( m1_subset_1(a_4_0_relset_2(sK6,sK7,sK8,sK9),k1_zfmisc_1(k1_zfmisc_1(sK7)))
| ~ spl342_48 ),
inference(resolution,[],[f11282,f6831]) ).
fof(f11556,plain,
( $false
| ~ spl342_48 ),
inference(forward_subsumption_resolution,[],[f11554,f6790]) ).
fof(f11557,plain,
~ spl342_48,
inference(avatar_contradiction_clause,[],[f11556]) ).
cnf(s36,plain,
( ~ spl342_46
| ~ spl342_47
| spl342_48 ),
inference(sat_conversion,[],[f11197]) ).
cnf(s38,plain,
spl342_46,
inference(sat_conversion,[],[f11204]) ).
cnf(s40,plain,
spl342_47,
inference(sat_conversion,[],[f11209]) ).
cnf(s78,plain,
~ spl342_48,
inference(sat_conversion,[],[f11557]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s36,s78,s40,s38]) ).
fof(f11558,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU424+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n008.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 05:21:40 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.19/2.45 % (1933405)Detected formulas, will run a generic FOF schedule.
% 10.19/2.45 % (1933411)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3335994251:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 10.19/2.45 % (1933412)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2019059964:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 10.19/2.45 % (1933416)dis-21_1_sil=8000:lcm=predicate:random_seed=3172049796:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 10.19/2.45 % (1933414)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3500408237:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 10.19/2.45 % (1933410)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2943668941:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 10.19/2.45 % (1933413)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=565585040:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 10.19/2.45 % (1933415)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2610544692:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 10.19/2.45 % (1933413)Instruction limit reached!
% 10.19/2.45 % (1933413)------------------------------
% 10.19/2.45 % (1933413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933413)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933413)Termination reason: Instruction limit
% 10.19/2.45 % (1933413)Termination phase: Saturation
% 10.19/2.45 % (1933413)Time elapsed: 0.062 s
% 10.19/2.45 % (1933413)Peak memory usage: 93 MB
% 10.19/2.45 % (1933413)Instructions burned: 109 (million)
% 10.19/2.45 % (1933414)Instruction limit reached!
% 10.19/2.45 % (1933414)------------------------------
% 10.19/2.45 % (1933414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933414)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933414)Termination reason: Instruction limit
% 10.19/2.45 % (1933414)Termination phase: Saturation
% 10.19/2.45 % (1933414)Time elapsed: 0.077 s
% 10.19/2.45 % (1933414)Peak memory usage: 94 MB
% 10.19/2.45 % (1933414)Instructions burned: 119 (million)
% 10.19/2.45 % (1933416)Instruction limit reached!
% 10.19/2.45 % (1933416)------------------------------
% 10.19/2.45 % (1933416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933416)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933416)Termination reason: Instruction limit
% 10.19/2.45 % (1933416)Termination phase: Clausification
% 10.19/2.45 % (1933416)Time elapsed: 0.089 s
% 10.19/2.45 % (1933416)Peak memory usage: 95 MB
% 10.19/2.45 % (1933416)Instructions burned: 129 (million)
% 10.19/2.45 % (1933415)Instruction limit reached!
% 10.19/2.45 % (1933415)------------------------------
% 10.19/2.45 % (1933415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933415)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933415)Termination reason: Instruction limit
% 10.19/2.45 % (1933415)Termination phase: Preprocessing 3
% 10.19/2.45 % (1933415)Time elapsed: 0.088 s
% 10.19/2.45 % (1933415)Peak memory usage: 94 MB
% 10.19/2.45 % (1933415)Instructions burned: 140 (million)
% 10.19/2.45 % (1933424)lrs+10_1_sil=8000:sp=occurrence:random_seed=3002770663:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 10.19/2.45 % (1933425)lrs+10_1_sil=32000:urr=on:br=off:random_seed=545085765:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 10.19/2.45 % (1933426)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2548529840:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 10.19/2.45 % (1933427)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1694628104:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 10.19/2.45 % (1933425)Instruction limit reached!
% 10.19/2.45 % (1933425)------------------------------
% 10.19/2.45 % (1933425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933425)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933425)Termination reason: Instruction limit
% 10.19/2.45 % (1933425)Termination phase: Saturation
% 10.19/2.45 % (1933425)Time elapsed: 0.088 s
% 10.19/2.45 % (1933425)Peak memory usage: 94 MB
% 10.19/2.45 % (1933425)Instructions burned: 158 (million)
% 10.19/2.45 % (1933427)Instruction limit reached!
% 10.19/2.45 % (1933427)------------------------------
% 10.19/2.45 % (1933427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933427)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933427)Termination reason: Instruction limit
% 10.19/2.45 % (1933427)Termination phase: Property scanning
% 10.19/2.45 % (1933427)Time elapsed: 0.141 s
% 10.19/2.45 % (1933427)Peak memory usage: 98 MB
% 10.19/2.45 % (1933427)Instructions burned: 248 (million)
% 10.19/2.45 % (1933424)Instruction limit reached!
% 10.19/2.45 % (1933424)------------------------------
% 10.19/2.45 % (1933424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933424)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933424)Termination reason: Instruction limit
% 10.19/2.45 % (1933424)Termination phase: Saturation
% 10.19/2.45 % (1933424)Time elapsed: 0.195 s
% 10.19/2.45 % (1933424)Peak memory usage: 97 MB
% 10.19/2.45 % (1933424)Instructions burned: 286 (million)
% 10.19/2.45 % (1933432)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3662443435:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 10.19/2.45 % (1933426)Instruction limit reached!
% 10.19/2.45 % (1933426)------------------------------
% 10.19/2.45 % (1933426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933426)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933426)Termination reason: Instruction limit
% 10.19/2.45 % (1933426)Termination phase: Saturation
% 10.19/2.45 % (1933426)Time elapsed: 0.241 s
% 10.19/2.45 % (1933426)Peak memory usage: 95 MB
% 10.19/2.45 % (1933426)Instructions burned: 326 (million)
% 10.19/2.45 % (1933433)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1597695597:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 10.19/2.45 % (1933434)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=114322268:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 10.19/2.45 % (1933437)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1763803228:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 10.19/2.45 % (1933434)Instruction limit reached!
% 10.19/2.45 % (1933434)------------------------------
% 10.19/2.45 % (1933434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933434)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933434)Termination reason: Instruction limit
% 10.19/2.45 % (1933434)Termination phase: Saturation
% 10.19/2.45 % (1933434)Time elapsed: 0.070 s
% 10.19/2.45 % (1933434)Peak memory usage: 95 MB
% 10.19/2.45 % (1933434)Instructions burned: 113 (million)
% 10.19/2.45 % (1933432)Instruction limit reached!
% 10.19/2.45 % (1933432)------------------------------
% 10.19/2.45 % (1933432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933432)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933432)Termination reason: Instruction limit
% 10.19/2.45 % (1933432)Termination phase: Saturation
% 10.19/2.45 % (1933432)Time elapsed: 0.174 s
% 10.19/2.45 % (1933432)Peak memory usage: 96 MB
% 10.19/2.45 % (1933432)Instructions burned: 295 (million)
% 10.19/2.45 % (1933437)Instruction limit reached!
% 10.19/2.45 % (1933437)------------------------------
% 10.19/2.45 % (1933437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933437)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933437)Termination reason: Instruction limit
% 10.19/2.45 % (1933437)Termination phase: Preprocessing 3
% 10.19/2.45 % (1933437)Time elapsed: 0.087 s
% 10.19/2.45 % (1933437)Peak memory usage: 97 MB
% 10.19/2.45 % (1933437)Instructions burned: 128 (million)
% 10.19/2.45 % (1933440)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3442143110:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 10.19/2.45 % (1933441)lrs+10_1_sil=8000:sp=occurrence:random_seed=4279673569:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 10.19/2.45 % (1933440)Instruction limit reached!
% 10.19/2.45 % (1933440)------------------------------
% 10.19/2.45 % (1933440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933440)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933440)Termination reason: Instruction limit
% 10.19/2.45 % (1933440)Termination phase: SInE selection
% 10.19/2.45 % (1933440)Time elapsed: 0.054 s
% 10.19/2.45 % (1933440)Peak memory usage: 89 MB
% 10.19/2.45 % (1933440)Instructions burned: 114 (million)
% 10.19/2.45 % (1933442)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1950576966:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 10.19/2.45 % (1933445)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2295086574:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 10.19/2.45 % (1933411)First to succeed.
% 10.19/2.45 % (1933411)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1933405"
% 10.19/2.45 % (1933442)Instruction limit reached!
% 10.19/2.45 % (1933442)------------------------------
% 10.19/2.45 % (1933442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.19/2.45 % (1933442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/2.45 % (1933442)CaDiCaL version: 2.1.3
% 10.19/2.45 % (1933442)Termination reason: Instruction limit
% 10.19/2.45 % (1933442)Termination phase: Saturation
% 10.19/2.45 % (1933442)Time elapsed: 0.287 s
% 10.19/2.45 % (1933442)Peak memory usage: 97 MB
% 10.19/2.45 % (1933442)Instructions burned: 437 (million)
% 10.19/2.45 % (1933448)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3517321704:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2985 on theBenchmark for (2985ds/134Mi)
% 10.19/2.45 % (1933411)Refutation found. Thanks to Tanya!
% 10.19/2.45 % SZS status Theorem for theBenchmark
% 10.19/2.45 % SZS output start Proof for theBenchmark
% See solution above
% 10.81/2.67 % (1933411)------------------------------
% 10.81/2.67 % (1933411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.81/2.67 % (1933411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.67 % (1933411)CaDiCaL version: 2.1.3
% 10.81/2.67 % (1933411)Termination reason: Refutation
% 10.81/2.67 % (1933411)Time elapsed: 1.045 s
% 10.81/2.67 % (1933411)Peak memory usage: 158 MB
% 10.81/2.67 % (1933411)Instructions burned: 2210 (million)
% 10.81/2.67 % (1933411)------------------------------
% 10.81/2.67 % (1933411)------------------------------
% 10.81/2.67 % (1933405)Success in time 1.596 s
% 10.81/2.67 % Vampire exiting
%------------------------------------------------------------------------------