%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU447+1 : 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 : n016.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 12:49:09 PM UTC 2026
% Result : Theorem 2.70s 1.28s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 81 ( 7 unt; 0 def)
% Number of atoms : 233 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 297 ( 145 ~; 120 |; 10 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-5 aty)
% Number of variables : 203 ( 197 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X0))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ! [X5] :
( m2_relset_1(X5,X1,X2)
=> k8_relset_2(X1,X2,k10_relset_1(X0,X1,X4,X3),X5) = k8_relset_2(X0,X2,X3,k3_subset_1(k2_zfmisc_1(X0,X2),k9_relset_2(X0,X1,X2,X4,k3_subset_1(k2_zfmisc_1(X1,X2),X5)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_relset_2) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X0))
=> ! [X4] :
( m2_relset_1(X4,X0,X1)
=> ! [X5] :
( m2_relset_1(X5,X1,X2)
=> k8_relset_2(X1,X2,k10_relset_1(X0,X1,X4,X3),X5) = k8_relset_2(X0,X2,X3,k3_subset_1(k2_zfmisc_1(X0,X2),k9_relset_2(X0,X1,X2,X4,k3_subset_1(k2_zfmisc_1(X1,X2),X5)))) ) ) ),
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(f7,axiom,
! [X0,X1,X2,X3] :
( m1_relset_1(X2,X0,X1)
=> m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
fof(f12,axiom,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> m1_subset_1(k3_subset_1(X0,X1),k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X0))
& m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
=> m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
=> m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relset_2) ).
fof(f25,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f37,axiom,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> k3_subset_1(X0,k3_subset_1(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f44,axiom,
! [X0,X1,X2,X3] :
( m1_relset_1(X2,X0,X1)
=> k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
fof(f48,axiom,
! [X0,X1,X2,X3,X4] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
=> k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
fof(f49,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(f51,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
fof(f55,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> k3_subset_1(X1,k8_relset_2(X0,X1,X2,X3)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(X0,X1),X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relset_2) ).
fof(f57,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> k3_subset_1(X1,k10_relset_1(X0,X1,X3,X2)) = k8_relset_2(X0,X1,X2,k3_subset_1(k2_zfmisc_1(X0,X1),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relset_2) ).
fof(f62,plain,
? [X0,X1,X2,X3] :
( ? [X4] :
( ? [X5] :
( k8_relset_2(X1,X2,k10_relset_1(X0,X1,X4,X3),X5) != k8_relset_2(X0,X2,X3,k3_subset_1(k2_zfmisc_1(X0,X2),k9_relset_2(X0,X1,X2,X4,k3_subset_1(k2_zfmisc_1(X1,X2),X5))))
& m2_relset_1(X5,X1,X2) )
& m2_relset_1(X4,X0,X1) )
& m1_subset_1(X3,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ! [X3] :
( k3_subset_1(X1,k10_relset_1(X0,X1,X3,X2)) = k8_relset_2(X0,X1,X2,k3_subset_1(k2_zfmisc_1(X0,X1),X3))
| ~ m2_relset_1(X3,X0,X1) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f67,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(flattening,[],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( k3_subset_1(X0,k3_subset_1(X0,X1)) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f73,plain,
! [X0,X1] :
( m1_subset_1(k3_subset_1(X0,X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4] :
( k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(ennf_transformation,[],[f21]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(flattening,[],[f76]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ! [X3] :
( k3_subset_1(X1,k8_relset_2(X0,X1,X2,X3)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(X0,X1),X3),X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0))
| ~ v1_relat_1(X2) )
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f87,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f89,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k8_relset_2(sK0,sK2,sK3,k3_subset_1(k2_zfmisc_1(sK0,sK2),k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5))))
& m2_relset_1(sK5,sK1,sK2)
& m2_relset_1(sK4,sK0,sK1)
& m1_subset_1(sK3,k1_zfmisc_1(sK0)) ),
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)],[f62]) ).
fof(f94,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,[],[f49]) ).
fof(f98,plain,
m1_subset_1(sK3,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f89]) ).
fof(f99,plain,
m2_relset_1(sK4,sK0,sK1),
inference(cnf_transformation,[],[f89]) ).
fof(f100,plain,
m2_relset_1(sK5,sK1,sK2),
inference(cnf_transformation,[],[f89]) ).
fof(f101,plain,
k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k8_relset_2(sK0,sK2,sK3,k3_subset_1(k2_zfmisc_1(sK0,sK2),k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)))),
inference(cnf_transformation,[],[f89]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( k3_subset_1(X1,k10_relset_1(X0,X1,X3,X2)) = k8_relset_2(X0,X1,X2,k3_subset_1(k2_zfmisc_1(X0,X1),X3))
| ~ m2_relset_1(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f108,plain,
! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f69]) ).
fof(f111,plain,
! [X0,X1] :
( k3_subset_1(X0,k3_subset_1(X0,X1)) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f112,plain,
! [X0,X1] :
( m1_subset_1(k3_subset_1(X0,X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( k9_relset_2(X0,X1,X2,X3,X4) = k5_relat_1(X3,X4)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X4] :
( m2_relset_1(k9_relset_2(X0,X1,X2,X3,X4),X0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[],[f77]) ).
fof(f120,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f121,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( k3_subset_1(X1,k8_relset_2(X0,X1,X2,X3)) = k9_relat_1(k3_subset_1(k2_zfmisc_1(X0,X1),X3),X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f124,plain,
! [X2,X0,X1] :
( k9_relat_1(k5_relat_1(X1,X2),X0) = k9_relat_1(X2,k9_relat_1(X1,X0))
| ~ v1_relat_1(X2)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_relat_1(X0) ),
inference(resolution,[],[f108,f135]) ).
fof(f143,plain,
v1_relat_1(sK4),
inference(resolution,[],[f140,f99]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k9_relat_1(X0,X1),k1_zfmisc_1(X3))
| ~ m1_relset_1(X0,X2,X3)
| ~ m1_relset_1(X0,X2,X3) ),
inference(superposition,[],[f106,f105]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k9_relat_1(X0,X1),k1_zfmisc_1(X3))
| ~ m1_relset_1(X0,X2,X3) ),
inference(duplicate_literal_removal,[],[f148]) ).
fof(f159,plain,
! [X2,X3,X0,X1,X4] :
( m2_relset_1(k5_relat_1(X0,X1),X2,X4)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4))) ),
inference(superposition,[],[f114,f113]) ).
fof(f160,plain,
! [X2,X3,X0,X1,X4] :
( m2_relset_1(k5_relat_1(X0,X1),X2,X4)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4))) ),
inference(duplicate_literal_removal,[],[f159]) ).
fof(f165,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k10_relset_1(sK0,sK2,k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK3))
| ~ m2_relset_1(k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK3,k1_zfmisc_1(sK0)) ),
inference(superposition,[],[f101,f104]) ).
fof(f170,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k10_relset_1(sK0,sK2,k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK3))
| ~ m2_relset_1(k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f165,f98]) ).
fof(f172,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k9_relat_1(k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK3))
| ~ m2_relset_1(k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_relset_1(k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2) ),
inference(superposition,[],[f170,f105]) ).
fof(f173,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k9_relat_1(k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK3))
| ~ m1_relset_1(k9_relset_2(sK0,sK1,sK2,sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f172,f121]) ).
fof(f176,plain,
! [X2,X3,X0,X1] :
( k8_relset_2(X0,X1,X3,X2) = k3_subset_1(X1,k9_relat_1(k3_subset_1(k2_zfmisc_1(X0,X1),X2),X3))
| ~ m1_subset_1(k8_relset_2(X0,X1,X3,X2),k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(X0)) ),
inference(superposition,[],[f111,f123]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( k8_relset_2(X0,X1,X3,X2) = k3_subset_1(X1,k9_relat_1(k3_subset_1(k2_zfmisc_1(X0,X1),X2),X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X3,k1_zfmisc_1(X0)) ),
inference(forward_subsumption_resolution,[],[f176,f109]) ).
fof(f181,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k9_relat_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK3))
| ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))) ),
inference(superposition,[],[f173,f113]) ).
fof(f182,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k9_relat_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k9_relat_1(sK4,sK3)))
| ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ v1_relat_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5))
| ~ v1_relat_1(sK4) ),
inference(superposition,[],[f181,f124]) ).
fof(f183,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k9_relat_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k9_relat_1(sK4,sK3)))
| ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ v1_relat_1(sK4) ),
inference(forward_subsumption_resolution,[],[f182,f135]) ).
fof(f184,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k3_subset_1(sK2,k9_relat_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k9_relat_1(sK4,sK3)))
| ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))) ),
inference(forward_subsumption_resolution,[],[f183,f143]) ).
fof(f227,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k8_relset_2(sK1,sK2,k9_relat_1(sK4,sK3),sK5)
| ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_subset_1(k9_relat_1(sK4,sK3),k1_zfmisc_1(sK1)) ),
inference(superposition,[],[f184,f180]) ).
fof(f228,plain,
( k8_relset_2(sK1,sK2,k10_relset_1(sK0,sK1,sK4,sK3),sK5) != k8_relset_2(sK1,sK2,k9_relat_1(sK4,sK3),sK5)
| ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_subset_1(k9_relat_1(sK4,sK3),k1_zfmisc_1(sK1)) ),
inference(forward_subsumption_resolution,[],[f227,f112]) ).
fof(f233,plain,
( k8_relset_2(sK1,sK2,k9_relat_1(sK4,sK3),sK5) != k8_relset_2(sK1,sK2,k9_relat_1(sK4,sK3),sK5)
| ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_subset_1(k9_relat_1(sK4,sK3),k1_zfmisc_1(sK1))
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(superposition,[],[f228,f105]) ).
fof(f234,plain,
( ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_subset_1(k9_relat_1(sK4,sK3),k1_zfmisc_1(sK1))
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(trivial_inequality_removal,[],[f233]) ).
fof(f235,plain,
( ~ m1_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f234,f149]) ).
fof(f236,plain,
( ~ m2_relset_1(k5_relat_1(sK4,k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5)),sK0,sK2)
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_relset_1(sK4,sK0,sK1)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(resolution,[],[f235,f120]) ).
fof(f242,plain,
! [X0] :
( ~ m1_subset_1(k3_subset_1(k2_zfmisc_1(sK1,sK2),sK5),k1_zfmisc_1(k2_zfmisc_1(X0,sK2)))
| ~ m1_relset_1(sK4,sK0,sK1)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,X0)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))) ),
inference(resolution,[],[f236,f160]) ).
fof(f259,plain,
( ~ m1_relset_1(sK4,sK0,sK1)
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2))) ),
inference(resolution,[],[f242,f112]) ).
fof(f261,plain,
( ~ m1_subset_1(sK5,k1_zfmisc_1(k2_zfmisc_1(sK1,sK2)))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(duplicate_literal_removal,[],[f259]) ).
fof(f262,plain,
( ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_relset_1(sK4,sK0,sK1)
| ~ m2_relset_1(sK5,sK1,sK2) ),
inference(resolution,[],[f261,f108]) ).
fof(f263,plain,
( ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ m1_relset_1(sK4,sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f262,f100]) ).
fof(f302,plain,
( ~ m1_relset_1(sK4,sK0,sK1)
| ~ m2_relset_1(sK4,sK0,sK1) ),
inference(resolution,[],[f263,f108]) ).
fof(f303,plain,
~ m2_relset_1(sK4,sK0,sK1),
inference(forward_subsumption_resolution,[],[f302,f120]) ).
fof(f304,plain,
$false,
inference(forward_subsumption_resolution,[],[f303,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU447+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:38:48 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.70/1.28 % (3314497)Detected formulas, will run a generic FOF schedule.
% 2.70/1.28 % (3314502)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=1939433569:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.28 % (3314504)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=1733537559:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.28 % (3314503)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=1113051425:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.28 % (3314505)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3696023094:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.28 % (3314505)Refutation not found, incomplete strategy
% 2.70/1.28 % (3314505)------------------------------
% 2.70/1.28 % (3314505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (3314505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (3314505)CaDiCaL version: 2.1.3
% 2.70/1.28 % (3314505)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.28 % (3314505)Time elapsed: 0.003 s
% 2.70/1.28 % (3314505)Peak memory usage: 88 MB
% 2.70/1.28 % (3314505)Instructions burned: 2 (million)
% 2.70/1.28 % (3314507)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=779837928:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.28 % (3314506)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2853123043:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.28 % (3314508)dis-21_1_sil=8000:lcm=predicate:random_seed=1159076584:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.70/1.28 % (3314506)First to succeed.
% 2.70/1.28 % (3314506)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3314497"
% 2.70/1.28 % (3314507)Also succeeded, but the first one will report.
% 2.70/1.28 % (3314508)Instruction limit reached!
% 2.70/1.28 % (3314508)------------------------------
% 2.70/1.28 % (3314508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (3314508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (3314508)CaDiCaL version: 2.1.3
% 2.70/1.28 % (3314508)Termination reason: Instruction limit
% 2.70/1.28 % (3314508)Termination phase: Saturation
% 2.70/1.28 % (3314508)Time elapsed: 0.071 s
% 2.70/1.28 % (3314508)Peak memory usage: 90 MB
% 2.70/1.28 % (3314508)Instructions burned: 131 (million)
% 2.70/1.28 % (3314516)lrs+10_1_sil=8000:sp=occurrence:random_seed=3861957460:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.70/1.28 % (3314505)------------------------------
% 2.70/1.28 % (3314505)------------------------------
% 2.70/1.28 % (3314506)Refutation found. Thanks to Tanya!
% 2.70/1.28 % SZS status Theorem for theBenchmark
% 2.70/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.37 % (3314506)------------------------------
% 3.41/1.37 % (3314506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.37 % (3314506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.37 % (3314506)CaDiCaL version: 2.1.3
% 3.41/1.37 % (3314506)Termination reason: Refutation
% 3.41/1.37 % (3314506)Time elapsed: 0.012 s
% 3.41/1.37 % (3314506)Peak memory usage: 88 MB
% 3.41/1.37 % (3314506)Instructions burned: 17 (million)
% 3.41/1.37 % (3314506)------------------------------
% 3.41/1.37 % (3314506)------------------------------
% 3.41/1.37 % (3314497)Success in time 0.416 s
% 3.41/1.37 % Vampire exiting
%------------------------------------------------------------------------------