%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU427+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:48:57 PM UTC 2026
% Result : Theorem 6.75s 1.97s
% Output : Refutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 40 unt; 0 def)
% Number of atoms : 164 ( 66 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 128 ( 49 ~; 41 |; 19 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 152 ( 142 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X0))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X4),k3_pua2mss1(X2)) = k1_xboole_0
=> k8_relset_2(X0,X1,k4_subset_1(X0,X2,X3),X4) = k8_relset_2(X0,X1,X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_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(X0))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> ( k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X4),k3_pua2mss1(X2)) = k1_xboole_0
=> k8_relset_2(X0,X1,k4_subset_1(X0,X2,X3),X4) = k8_relset_2(X0,X1,X3,X4) ) ) ) ),
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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f8,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)))
=> k7_relset_2(X0,X1,X2,X3) = k8_setfam_1(X1,k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X3),k3_pua2mss1(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relset_2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X0))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> m1_subset_1(k4_subset_1(X0,X1,X2),k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
=> ( v1_funct_1(k6_relset_2(X0,X1,X2))
& v1_funct_2(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
& m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f44,axiom,
! [X0,X1,X2,X3] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1))))
=> k4_relset_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
fof(f45,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X0))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> k4_subset_1(X0,X1,X2) = k2_xboole_0(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(f46,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
=> k6_relset_2(X0,X1,X2) = k5_relset_2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
fof(f47,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))) )
=> k8_relset_2(X0,X1,X2,X3) = k7_relset_2(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
fof(f50,axiom,
! [X0,X1,X2] :
( v1_relat_1(X2)
=> k9_relat_1(X2,k2_xboole_0(X0,X1)) = k2_xboole_0(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_relat_1) ).
fof(f51,axiom,
! [X0] : k2_xboole_0(X0,k1_xboole_0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f54,axiom,
! [X0,X1] : k3_pua2mss1(k2_xboole_0(X0,X1)) = k2_xboole_0(k3_pua2mss1(X0),k3_pua2mss1(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relset_2) ).
fof(f63,plain,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( k8_relset_2(X0,X1,k4_subset_1(X0,X2,X3),X4) != k8_relset_2(X0,X1,X3,X4)
& k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X4),k3_pua2mss1(X2)) = k1_xboole_0
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
& m1_subset_1(X3,k1_zfmisc_1(X0)) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f64,plain,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( k8_relset_2(X0,X1,k4_subset_1(X0,X2,X3),X4) != k8_relset_2(X0,X1,X3,X4)
& k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X4),k3_pua2mss1(X2)) = k1_xboole_0
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
& m1_subset_1(X3,k1_zfmisc_1(X0)) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f63]) ).
fof(f67,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(f70,plain,
! [X0,X1,X2] :
( ! [X3] :
( k7_relset_2(X0,X1,X2,X3) = k8_setfam_1(X1,k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X3),k3_pua2mss1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f72,plain,
! [X0,X1,X2] :
( m1_subset_1(k4_subset_1(X0,X1,X2),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f73,plain,
! [X0,X1,X2] :
( m1_subset_1(k4_subset_1(X0,X1,X2),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f72]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( v1_funct_1(k6_relset_2(X0,X1,X2))
& v1_funct_2(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
& m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0)) )
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ),
inference(ennf_transformation,[],[f17]) ).
fof(f80,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(f88,plain,
! [X0,X1,X2,X3] :
( k4_relset_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1)))) ),
inference(ennf_transformation,[],[f44]) ).
fof(f89,plain,
! [X0,X1,X2] :
( k4_subset_1(X0,X1,X2) = k2_xboole_0(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f90,plain,
! [X0,X1,X2] :
( k4_subset_1(X0,X1,X2) = k2_xboole_0(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( k6_relset_2(X0,X1,X2) = k5_relset_2(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ),
inference(ennf_transformation,[],[f46]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( k8_relset_2(X0,X1,X2,X3) = k7_relset_2(X0,X1,X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f47]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( k8_relset_2(X0,X1,X2,X3) = k7_relset_2(X0,X1,X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( k9_relat_1(X2,k2_xboole_0(X0,X1)) = k2_xboole_0(k9_relat_1(X2,X0),k9_relat_1(X2,X1))
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f50]) ).
fof(f104,plain,
( k8_relset_2(sK0,sK1,k4_subset_1(sK0,sK2,sK3),sK4) != k8_relset_2(sK0,sK1,sK3,sK4)
& k1_xboole_0 = k4_relset_2(k1_zfmisc_1(sK0),sK1,k6_relset_2(sK1,sK0,sK4),k3_pua2mss1(sK2))
& m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
& m1_subset_1(sK3,k1_zfmisc_1(sK0))
& m1_subset_1(sK2,k1_zfmisc_1(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f64]) ).
fof(f117,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f104]) ).
fof(f118,plain,
m1_subset_1(sK3,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f104]) ).
fof(f119,plain,
m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))),
inference(cnf_transformation,[],[f104]) ).
fof(f120,plain,
k1_xboole_0 = k4_relset_2(k1_zfmisc_1(sK0),sK1,k6_relset_2(sK1,sK0,sK4),k3_pua2mss1(sK2)),
inference(cnf_transformation,[],[f104]) ).
fof(f121,plain,
k8_relset_2(sK0,sK1,k4_subset_1(sK0,sK2,sK3),sK4) != k8_relset_2(sK0,sK1,sK3,sK4),
inference(cnf_transformation,[],[f104]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| v1_relat_1(X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f125,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| k7_relset_2(X0,X1,X2,X3) = k8_setfam_1(X1,k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X3),k3_pua2mss1(X2)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| m1_subset_1(k4_subset_1(X0,X1,X2),k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f133,plain,
! [X2,X0,X1] :
( m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ),
inference(cnf_transformation,[],[f75]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1))))
| k4_relset_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
inference(cnf_transformation,[],[f88]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| k4_subset_1(X0,X1,X2) = k2_xboole_0(X1,X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
| k6_relset_2(X0,X1,X2) = k5_relset_2(X1,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| k7_relset_2(X0,X1,X2,X3) = k8_relset_2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f93]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X2)
| k9_relat_1(X2,k2_xboole_0(X0,X1)) = k2_xboole_0(k9_relat_1(X2,X0),k9_relat_1(X2,X1)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f176,plain,
! [X0] : k2_xboole_0(X0,k1_xboole_0) = X0,
inference(cnf_transformation,[],[f51]) ).
fof(f179,plain,
! [X0,X1] : k3_pua2mss1(k2_xboole_0(X0,X1)) = k2_xboole_0(k3_pua2mss1(X0),k3_pua2mss1(X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f187,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| k7_relset_2(sK0,sK1,X0,sK4) = k8_relset_2(sK0,sK1,X0,sK4) ),
inference(resolution,[],[f171,f119]) ).
fof(f188,plain,
k6_relset_2(sK1,sK0,sK4) = k5_relset_2(sK0,sK4),
inference(resolution,[],[f170,f119]) ).
fof(f189,plain,
( m2_relset_1(k5_relset_2(sK0,sK4),k1_zfmisc_1(sK0),k1_zfmisc_1(sK1))
| ~ m1_subset_1(sK4,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))) ),
inference(superposition,[],[f133,f188]) ).
fof(f190,plain,
m2_relset_1(k5_relset_2(sK0,sK4),k1_zfmisc_1(sK0),k1_zfmisc_1(sK1)),
inference(forward_subsumption_resolution,[],[f189,f119]) ).
fof(f192,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| k4_subset_1(sK0,X0,sK2) = k2_xboole_0(X0,sK2) ),
inference(resolution,[],[f169,f117]) ).
fof(f193,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| k4_subset_1(sK0,X0,sK3) = k2_xboole_0(X0,sK3) ),
inference(resolution,[],[f169,f118]) ).
fof(f202,plain,
! [X0] :
( k7_relset_2(sK0,sK1,X0,sK4) = k8_setfam_1(sK1,k4_relset_2(k1_zfmisc_1(sK0),sK1,k6_relset_2(sK1,sK0,sK4),k3_pua2mss1(X0)))
| ~ m1_subset_1(X0,k1_zfmisc_1(sK0)) ),
inference(resolution,[],[f127,f119]) ).
fof(f203,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| k7_relset_2(sK0,sK1,X0,sK4) = k8_setfam_1(sK1,k4_relset_2(k1_zfmisc_1(sK0),sK1,k5_relset_2(sK0,sK4),k3_pua2mss1(X0))) ),
inference(forward_demodulation,[],[f202,f188]) ).
fof(f205,plain,
k8_relset_2(sK0,sK1,sK3,sK4) = k7_relset_2(sK0,sK1,sK3,sK4),
inference(resolution,[],[f187,f118]) ).
fof(f207,plain,
k7_relset_2(sK0,sK1,sK3,sK4) = k8_setfam_1(sK1,k4_relset_2(k1_zfmisc_1(sK0),sK1,k5_relset_2(sK0,sK4),k3_pua2mss1(sK3))),
inference(resolution,[],[f203,f118]) ).
fof(f208,plain,
k1_xboole_0 = k4_relset_2(k1_zfmisc_1(sK0),sK1,k5_relset_2(sK0,sK4),k3_pua2mss1(sK2)),
inference(superposition,[],[f120,f188]) ).
fof(f219,plain,
! [X0] :
( ~ m1_subset_1(X0,k1_zfmisc_1(sK0))
| m1_subset_1(k4_subset_1(sK0,X0,sK2),k1_zfmisc_1(sK0)) ),
inference(resolution,[],[f130,f117]) ).
fof(f223,plain,
k4_subset_1(sK0,sK3,sK2) = k2_xboole_0(sK3,sK2),
inference(resolution,[],[f192,f118]) ).
fof(f224,plain,
k4_subset_1(sK0,sK3,sK2) = k2_xboole_0(sK2,sK3),
inference(forward_demodulation,[],[f223,f125]) ).
fof(f228,plain,
m1_subset_1(k5_relset_2(sK0,sK4),k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(sK0),k1_zfmisc_1(sK1)))),
inference(resolution,[],[f139,f190]) ).
fof(f236,plain,
! [X0] : k4_relset_2(k1_zfmisc_1(sK0),sK1,k5_relset_2(sK0,sK4),X0) = k9_relat_1(k5_relset_2(sK0,sK4),X0),
inference(resolution,[],[f228,f168]) ).
fof(f238,plain,
v1_relat_1(k5_relset_2(sK0,sK4)),
inference(resolution,[],[f228,f124]) ).
fof(f246,plain,
! [X0,X1] : k9_relat_1(k5_relset_2(sK0,sK4),k2_xboole_0(X0,X1)) = k2_xboole_0(k9_relat_1(k5_relset_2(sK0,sK4),X0),k9_relat_1(k5_relset_2(sK0,sK4),X1)),
inference(resolution,[],[f238,f175]) ).
fof(f247,plain,
k7_relset_2(sK0,sK1,sK3,sK4) = k8_setfam_1(sK1,k9_relat_1(k5_relset_2(sK0,sK4),k3_pua2mss1(sK3))),
inference(superposition,[],[f207,f236]) ).
fof(f254,plain,
k4_subset_1(sK0,sK2,sK3) = k2_xboole_0(sK2,sK3),
inference(resolution,[],[f193,f117]) ).
fof(f257,plain,
k8_relset_2(sK0,sK1,sK3,sK4) != k8_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4),
inference(superposition,[],[f121,f254]) ).
fof(f258,plain,
k7_relset_2(sK0,sK1,sK3,sK4) != k8_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4),
inference(forward_demodulation,[],[f257,f205]) ).
fof(f268,plain,
! [X0] : k2_xboole_0(k1_xboole_0,X0) = X0,
inference(superposition,[],[f125,f176]) ).
fof(f310,plain,
k1_xboole_0 = k9_relat_1(k5_relset_2(sK0,sK4),k3_pua2mss1(sK2)),
inference(superposition,[],[f236,f208]) ).
fof(f320,plain,
m1_subset_1(k4_subset_1(sK0,sK3,sK2),k1_zfmisc_1(sK0)),
inference(resolution,[],[f219,f118]) ).
fof(f321,plain,
m1_subset_1(k2_xboole_0(sK2,sK3),k1_zfmisc_1(sK0)),
inference(forward_demodulation,[],[f320,f224]) ).
fof(f323,plain,
k8_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4) = k7_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4),
inference(resolution,[],[f321,f187]) ).
fof(f329,plain,
k7_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4) = k8_setfam_1(sK1,k4_relset_2(k1_zfmisc_1(sK0),sK1,k5_relset_2(sK0,sK4),k3_pua2mss1(k2_xboole_0(sK2,sK3)))),
inference(resolution,[],[f321,f203]) ).
fof(f335,plain,
k7_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4) = k8_setfam_1(sK1,k9_relat_1(k5_relset_2(sK0,sK4),k3_pua2mss1(k2_xboole_0(sK2,sK3)))),
inference(forward_demodulation,[],[f329,f236]) ).
fof(f338,plain,
k7_relset_2(sK0,sK1,sK3,sK4) != k7_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4),
inference(superposition,[],[f258,f323]) ).
fof(f389,plain,
! [X0] : k9_relat_1(k5_relset_2(sK0,sK4),k2_xboole_0(k3_pua2mss1(sK2),X0)) = k2_xboole_0(k1_xboole_0,k9_relat_1(k5_relset_2(sK0,sK4),X0)),
inference(superposition,[],[f246,f310]) ).
fof(f396,plain,
! [X0] : k9_relat_1(k5_relset_2(sK0,sK4),X0) = k9_relat_1(k5_relset_2(sK0,sK4),k2_xboole_0(k3_pua2mss1(sK2),X0)),
inference(forward_demodulation,[],[f389,f268]) ).
fof(f397,plain,
! [X0] : k9_relat_1(k5_relset_2(sK0,sK4),k3_pua2mss1(X0)) = k9_relat_1(k5_relset_2(sK0,sK4),k3_pua2mss1(k2_xboole_0(sK2,X0))),
inference(superposition,[],[f396,f179]) ).
fof(f422,plain,
k8_setfam_1(sK1,k9_relat_1(k5_relset_2(sK0,sK4),k3_pua2mss1(sK3))) = k7_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4),
inference(superposition,[],[f335,f397]) ).
fof(f428,plain,
k7_relset_2(sK0,sK1,sK3,sK4) = k7_relset_2(sK0,sK1,k2_xboole_0(sK2,sK3),sK4),
inference(forward_demodulation,[],[f422,f247]) ).
fof(f430,plain,
$false,
inference(forward_subsumption_resolution,[],[f428,f338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU427+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.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
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:23:04 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.75/1.97 % (4054448)Detected formulas, will run a generic FOF schedule.
% 6.75/1.97 % (4054456)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3009800495:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.75/1.97 % (4054456)Refutation not found, incomplete strategy
% 6.75/1.97 % (4054456)------------------------------
% 6.75/1.97 % (4054456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054456)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054456)Termination reason: Refutation not found, incomplete strategy
% 6.75/1.97 % (4054456)Time elapsed: 0.002 s
% 6.75/1.97 % (4054456)Peak memory usage: 88 MB
% 6.75/1.97 % (4054456)Instructions burned: 2 (million)
% 6.75/1.97 % (4054454)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=3697718847:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.75/1.97 % (4054459)dis-21_1_sil=8000:lcm=predicate:random_seed=3261256042: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)
% 6.75/1.97 % (4054453)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=4081619919:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.75/1.97 % (4054455)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=1974970890:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.75/1.97 % (4054457)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2146776992:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.75/1.97 % (4054458)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1412910884:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.75/1.97 % (4054457)Instruction limit reached!
% 6.75/1.97 % (4054457)------------------------------
% 6.75/1.97 % (4054457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054457)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054457)Termination reason: Instruction limit
% 6.75/1.97 % (4054457)Termination phase: Saturation
% 6.75/1.97 % (4054457)Time elapsed: 0.064 s
% 6.75/1.97 % (4054457)Peak memory usage: 88 MB
% 6.75/1.97 % (4054457)Instructions burned: 121 (million)
% 6.75/1.97 % (4054459)Instruction limit reached!
% 6.75/1.97 % (4054459)------------------------------
% 6.75/1.97 % (4054459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054459)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054459)Termination reason: Instruction limit
% 6.75/1.97 % (4054459)Termination phase: Saturation
% 6.75/1.97 % (4054459)Time elapsed: 0.076 s
% 6.75/1.97 % (4054459)Peak memory usage: 89 MB
% 6.75/1.97 % (4054459)Instructions burned: 129 (million)
% 6.75/1.97 % (4054458)Instruction limit reached!
% 6.75/1.97 % (4054458)------------------------------
% 6.75/1.97 % (4054458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054458)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054458)Termination reason: Instruction limit
% 6.75/1.97 % (4054458)Termination phase: Saturation
% 6.75/1.97 % (4054458)Time elapsed: 0.095 s
% 6.75/1.97 % (4054458)Peak memory usage: 90 MB
% 6.75/1.97 % (4054458)Instructions burned: 140 (million)
% 6.75/1.97 % (4054456)------------------------------
% 6.75/1.97 % (4054456)------------------------------
% 6.75/1.97 % (4054467)lrs+10_1_sil=8000:sp=occurrence:random_seed=107821483:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.75/1.97 % (4054468)lrs+10_1_sil=32000:urr=on:br=off:random_seed=671956823:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.75/1.97 % (4054470)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=1616972706:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.75/1.97 % (4054469)lrs+1011_1_sil=32000:sp=occurrence:random_seed=254910801:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.75/1.97 % (4054468)Instruction limit reached!
% 6.75/1.97 % (4054468)------------------------------
% 6.75/1.97 % (4054468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054468)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054468)Termination reason: Instruction limit
% 6.75/1.97 % (4054468)Termination phase: Saturation
% 6.75/1.97 % (4054468)Time elapsed: 0.075 s
% 6.75/1.97 % (4054468)Peak memory usage: 89 MB
% 6.75/1.97 % (4054468)Instructions burned: 159 (million)
% 6.75/1.97 % (4054470)Instruction limit reached!
% 6.75/1.97 % (4054470)------------------------------
% 6.75/1.97 % (4054470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054470)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054470)Termination reason: Instruction limit
% 6.75/1.97 % (4054470)Termination phase: Saturation
% 6.75/1.97 % (4054470)Time elapsed: 0.074 s
% 6.75/1.97 % (4054470)Peak memory usage: 93 MB
% 6.75/1.97 % (4054470)Instructions burned: 252 (million)
% 6.75/1.97 % (4054467)Instruction limit reached!
% 6.75/1.97 % (4054467)------------------------------
% 6.75/1.97 % (4054467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054467)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054467)Termination reason: Instruction limit
% 6.75/1.97 % (4054467)Termination phase: Saturation
% 6.75/1.97 % (4054467)Time elapsed: 0.181 s
% 6.75/1.97 % (4054467)Peak memory usage: 93 MB
% 6.75/1.97 % (4054467)Instructions burned: 286 (million)
% 6.75/1.97 % (4054476)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3979375964:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.75/1.97 % (4054475)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3593818596:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.75/1.97 % (4054469)Instruction limit reached!
% 6.75/1.97 % (4054469)------------------------------
% 6.75/1.97 % (4054469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054469)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054469)Termination reason: Instruction limit
% 6.75/1.97 % (4054469)Termination phase: Saturation
% 6.75/1.97 % (4054469)Time elapsed: 0.202 s
% 6.75/1.97 % (4054469)Peak memory usage: 92 MB
% 6.75/1.97 % (4054469)Instructions burned: 327 (million)
% 6.75/1.97 % (4054477)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3303281608:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.75/1.97 % (4054475)Instruction limit reached!
% 6.75/1.97 % (4054475)------------------------------
% 6.75/1.97 % (4054475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054475)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054475)Termination reason: Instruction limit
% 6.75/1.97 % (4054475)Termination phase: Saturation
% 6.75/1.97 % (4054475)Time elapsed: 0.161 s
% 6.75/1.97 % (4054475)Peak memory usage: 89 MB
% 6.75/1.97 % (4054475)Instructions burned: 294 (million)
% 6.75/1.97 % (4054480)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3979047519:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.75/1.97 % (4054477)Instruction limit reached!
% 6.75/1.97 % (4054477)------------------------------
% 6.75/1.97 % (4054477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054477)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054477)Termination reason: Instruction limit
% 6.75/1.97 % (4054477)Termination phase: Saturation
% 6.75/1.97 % (4054477)Time elapsed: 0.086 s
% 6.75/1.97 % (4054477)Peak memory usage: 90 MB
% 6.75/1.97 % (4054477)Instructions burned: 113 (million)
% 6.75/1.97 % (4054454)First to succeed.
% 6.75/1.97 % (4054454)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4054448"
% 6.75/1.97 % (4054480)Instruction limit reached!
% 6.75/1.97 % (4054480)------------------------------
% 6.75/1.97 % (4054480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054480)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054480)Termination reason: Instruction limit
% 6.75/1.97 % (4054480)Termination phase: Saturation
% 6.75/1.97 % (4054480)Time elapsed: 0.065 s
% 6.75/1.97 % (4054480)Peak memory usage: 89 MB
% 6.75/1.97 % (4054480)Instructions burned: 128 (million)
% 6.75/1.97 % (4054482)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=868162189:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.75/1.97 % (4054453)Also succeeded, but the first one will report.
% 6.75/1.97 % (4054484)lrs+10_1_sil=8000:sp=occurrence:random_seed=718571057:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.75/1.97 % (4054482)Instruction limit reached!
% 6.75/1.97 % (4054482)------------------------------
% 6.75/1.97 % (4054482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.75/1.97 % (4054482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.75/1.97 % (4054482)CaDiCaL version: 2.1.3
% 6.75/1.97 % (4054482)Termination reason: Instruction limit
% 6.75/1.97 % (4054482)Termination phase: Saturation
% 6.75/1.97 % (4054482)Time elapsed: 0.061 s
% 6.75/1.97 % (4054482)Peak memory usage: 89 MB
% 6.75/1.97 % (4054482)Instructions burned: 114 (million)
% 6.75/1.97 % (4054485)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2848255837:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.75/1.97 % (4054476)Also succeeded, but the first one will report.
% 6.75/1.97 % (4054454)Refutation found. Thanks to Tanya!
% 6.75/1.97 % SZS status Theorem for theBenchmark
% 6.75/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 8.41/2.17 % (4054454)------------------------------
% 8.41/2.17 % (4054454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.41/2.17 % (4054454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/2.17 % (4054454)CaDiCaL version: 2.1.3
% 8.41/2.17 % (4054454)Termination reason: Refutation
% 8.41/2.17 % (4054454)Time elapsed: 0.679 s
% 8.41/2.17 % (4054454)Peak memory usage: 127 MB
% 8.41/2.17 % (4054454)Instructions burned: 1002 (million)
% 8.41/2.17 % (4054454)------------------------------
% 8.41/2.17 % (4054454)------------------------------
% 8.41/2.17 % (4054448)Success in time 1.109 s
% 8.41/2.17 % Vampire exiting
%------------------------------------------------------------------------------