%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU411+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 : 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 12:48:48 PM UTC 2026
% Result : Theorem 2.27s 1.16s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 14 unt; 0 def)
% Number of atoms : 399 ( 10 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 515 ( 183 ~; 163 |; 142 &)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 129 ( 117 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_yellow_0(X0)
& v1_lattice3(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_yellow_0(X0)
& v1_lattice3(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v12_waybel_0(X1,X0)
<=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( ( r2_hidden(X2,X1)
& r1_orders_2(X0,X3,X2) )
=> r2_hidden(X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_waybel_0) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = k3_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f11,axiom,
! [X0] :
( l1_orders_2(X0)
=> m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
fof(f18,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f33,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( v1_xboole_0(X1)
| r2_hidden(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f35,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v4_orders_2(X0)
& v1_yellow_0(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r1_orders_2(X0,k3_yellow_0(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( r2_hidden(X0,X1)
& m1_subset_1(X1,k1_zfmisc_1(X2)) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f43,plain,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_yellow_0(X0)
& v1_lattice3(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
inference(pure_predicate_removal,[],[f2]) ).
fof(f44,plain,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_yellow_0(X0)
& l1_orders_2(X0) )
=> ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& l1_orders_2(X1) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
inference(pure_predicate_removal,[],[f43]) ).
fof(f45,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(X0))
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& l1_orders_2(X1) )
& ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_yellow_0(X0)
& l1_orders_2(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(X0))
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& l1_orders_2(X1) )
& ~ v3_struct_0(X0)
& v2_orders_2(X0)
& v3_orders_2(X0)
& v4_orders_2(X0)
& v1_yellow_0(X0)
& l1_orders_2(X0) ),
inference(flattening,[],[f45]) ).
fof(f50,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(ennf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0] :
( m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( r1_orders_2(X0,k3_yellow_0(X0),X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v4_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( r1_orders_2(X0,k3_yellow_0(X0),X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| v3_struct_0(X0)
| ~ v4_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( v12_waybel_0(X1,X0)
<=> ! [X2] :
( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X2,X1)
| ~ r1_orders_2(X0,X3,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) ) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( v12_waybel_0(X1,X0)
<=> ! [X2] :
( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X2,X1)
| ~ r1_orders_2(X0,X3,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) ) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f60]) ).
fof(f65,plain,
( ~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0))
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v3_struct_0(sK1)
& v2_orders_2(sK1)
& v3_orders_2(sK1)
& v4_orders_2(sK1)
& v1_yellow_0(sK1)
& l1_orders_2(sK1)
& ~ v3_struct_0(sK0)
& v2_orders_2(sK0)
& v3_orders_2(sK0)
& v4_orders_2(sK0)
& v1_yellow_0(sK0)
& l1_orders_2(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f46]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ? [X3] :
( ( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ? [X3] :
( ( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X3] :
( ( r2_hidden(X3,X2)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ? [X3] :
( ( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X0)
& r2_hidden(X3,X1) )
| r2_hidden(X3,X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| ~ r2_hidden(X4,X1) )
& ( ( r2_hidden(X4,X0)
& r2_hidden(X4,X1) )
| ~ r2_hidden(X4,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( X2 = k3_xboole_0(X0,X1)
| ( ( ~ r2_hidden(sK2(X0,X1,X2),X0)
| ~ r2_hidden(sK2(X0,X1,X2),X1)
| ~ r2_hidden(sK2(X0,X1,X2),X2) )
& ( ( r2_hidden(sK2(X0,X1,X2),X0)
& r2_hidden(sK2(X0,X1,X2),X1) )
| r2_hidden(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X0)
| ~ r2_hidden(X4,X1) )
& ( ( r2_hidden(X4,X0)
& r2_hidden(X4,X1) )
| ~ r2_hidden(X4,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f68]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ( v12_waybel_0(X1,X0)
| ? [X2] :
( ? [X3] :
( ~ r2_hidden(X3,X1)
& r2_hidden(X2,X1)
& r1_orders_2(X0,X3,X2)
& m1_subset_1(X3,u1_struct_0(X0)) )
& m1_subset_1(X2,u1_struct_0(X0)) ) )
& ( ! [X2] :
( ! [X3] :
( r2_hidden(X3,X1)
| ~ r2_hidden(X2,X1)
| ~ r1_orders_2(X0,X3,X2)
| ~ m1_subset_1(X3,u1_struct_0(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ v12_waybel_0(X1,X0) ) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_orders_2(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ( v12_waybel_0(X1,X0)
| ? [X2] :
( ? [X3] :
( ~ r2_hidden(X3,X1)
& r2_hidden(X2,X1)
& r1_orders_2(X0,X3,X2)
& m1_subset_1(X3,u1_struct_0(X0)) )
& m1_subset_1(X2,u1_struct_0(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(X4,X1)
| ~ r1_orders_2(X0,X5,X4)
| ~ m1_subset_1(X5,u1_struct_0(X0)) )
| ~ m1_subset_1(X4,u1_struct_0(X0)) )
| ~ v12_waybel_0(X1,X0) ) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_orders_2(X0) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( ( v12_waybel_0(X1,X0)
| ( ~ r2_hidden(sK8(X0,X1),X1)
& r2_hidden(sK7(X0,X1),X1)
& r1_orders_2(X0,sK8(X0,X1),sK7(X0,X1))
& m1_subset_1(sK8(X0,X1),u1_struct_0(X0))
& m1_subset_1(sK7(X0,X1),u1_struct_0(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(X4,X1)
| ~ r1_orders_2(X0,X5,X4)
| ~ m1_subset_1(X5,u1_struct_0(X0)) )
| ~ m1_subset_1(X4,u1_struct_0(X0)) )
| ~ v12_waybel_0(X1,X0) ) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_orders_2(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1))],[f75]) ).
fof(f77,plain,
! [X0] : m1_subset_1(sK9(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f18]) ).
fof(f84,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f85,plain,
v1_yellow_0(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f86,plain,
v4_orders_2(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f89,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f65]) ).
fof(f91,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f92,plain,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),
inference(cnf_transformation,[],[f65]) ).
fof(f93,plain,
~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0)),
inference(cnf_transformation,[],[f65]) ).
fof(f97,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X0)
| ~ r2_hidden(X4,X2)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f69]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f108,plain,
! [X0] :
( m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f109,plain,
! [X0,X1] :
( r1_orders_2(X0,k3_yellow_0(X0),X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| v3_struct_0(X0)
| ~ v4_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f113,plain,
! [X0,X1,X4,X5] :
( r2_hidden(X5,X1)
| ~ r2_hidden(X4,X1)
| ~ r1_orders_2(X0,X5,X4)
| ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ m1_subset_1(X4,u1_struct_0(X0))
| ~ v12_waybel_0(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f119,plain,
! [X0] : m1_subset_1(sK9(X0),X0),
inference(cnf_transformation,[],[f77]) ).
fof(f121,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f126,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k3_xboole_0(X0,X1))
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f97]) ).
fof(f152,plain,
! [X0] :
( ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(resolution,[],[f104,f90]) ).
fof(f154,plain,
! [X0] :
( m1_subset_1(X0,u1_struct_0(sK1))
| v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ m1_subset_1(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ),
inference(resolution,[],[f152,f121]) ).
fof(f155,plain,
! [X0] :
( ~ m1_subset_1(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f154,f92]) ).
fof(f157,plain,
m1_subset_1(sK9(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1)),
inference(resolution,[],[f155,f119]) ).
fof(f270,plain,
! [X0,X1,X4,X5] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ r2_hidden(X4,X1)
| ~ r1_orders_2(X0,X5,X4)
| ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ v12_waybel_0(X1,X0)
| r2_hidden(X5,X1)
| ~ l1_orders_2(X0) ),
inference(forward_subsumption_resolution,[],[f113,f104]) ).
fof(f274,plain,
! [X0,X1] :
( ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ r1_orders_2(sK1,X1,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
| r2_hidden(X1,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ l1_orders_2(sK1) ),
inference(resolution,[],[f270,f90]) ).
fof(f279,plain,
! [X0,X1] :
( ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ r1_orders_2(sK1,X1,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| r2_hidden(X1,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ l1_orders_2(sK1) ),
inference(forward_subsumption_resolution,[],[f274,f91]) ).
fof(f280,plain,
! [X0,X1] :
( r2_hidden(X1,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ r1_orders_2(sK1,X1,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[],[f279,f84]) ).
fof(f286,plain,
! [X0,X1] :
( ~ r2_hidden(X1,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ r1_orders_2(sK1,X0,X1)
| r2_hidden(X0,u1_struct_0(sK0)) ),
inference(resolution,[],[f280,f126]) ).
fof(f304,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ r1_orders_2(sK1,X0,X1)
| r2_hidden(X0,u1_struct_0(sK0))
| v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ m1_subset_1(X1,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ),
inference(resolution,[],[f286,f121]) ).
fof(f308,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ r1_orders_2(sK1,X0,X1)
| r2_hidden(X0,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(forward_subsumption_resolution,[],[f304,f92]) ).
fof(f366,plain,
! [X0] :
( ~ r1_orders_2(sK1,X0,sK9(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))))
| r2_hidden(X0,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(resolution,[],[f308,f119]) ).
fof(f385,plain,
( r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0))
| ~ m1_subset_1(k3_yellow_0(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(sK9(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1))
| v3_struct_0(sK1)
| ~ v4_orders_2(sK1)
| ~ v1_yellow_0(sK1)
| ~ l1_orders_2(sK1) ),
inference(resolution,[],[f366,f109]) ).
fof(f386,plain,
( ~ m1_subset_1(k3_yellow_0(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(sK9(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1))
| v3_struct_0(sK1)
| ~ v4_orders_2(sK1)
| ~ v1_yellow_0(sK1)
| ~ l1_orders_2(sK1) ),
inference(forward_subsumption_resolution,[],[f385,f93]) ).
fof(f387,plain,
( ~ m1_subset_1(sK9(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1))
| v3_struct_0(sK1)
| ~ v4_orders_2(sK1)
| ~ v1_yellow_0(sK1)
| ~ l1_orders_2(sK1) ),
inference(forward_subsumption_resolution,[],[f386,f108]) ).
fof(f388,plain,
( v3_struct_0(sK1)
| ~ v4_orders_2(sK1)
| ~ v1_yellow_0(sK1)
| ~ l1_orders_2(sK1) ),
inference(forward_subsumption_resolution,[],[f387,f157]) ).
fof(f389,plain,
( ~ v4_orders_2(sK1)
| ~ v1_yellow_0(sK1)
| ~ l1_orders_2(sK1) ),
inference(forward_subsumption_resolution,[],[f388,f89]) ).
fof(f390,plain,
( ~ v1_yellow_0(sK1)
| ~ l1_orders_2(sK1) ),
inference(forward_subsumption_resolution,[],[f389,f86]) ).
fof(f391,plain,
~ l1_orders_2(sK1),
inference(forward_subsumption_resolution,[],[f390,f85]) ).
fof(f392,plain,
$false,
inference(forward_subsumption_resolution,[],[f391,f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU411+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % 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 05:14:24 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.27/1.16 % (1898966)Detected formulas, will run a generic FOF schedule.
% 2.27/1.16 % (1898975)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1522682880:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.27/1.16 % (1898975)First to succeed.
% 2.27/1.16 % (1898975)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1898966"
% 2.27/1.16 % (1898972)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=1807141229:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.27/1.16 % (1898971)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=1220974654:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.27/1.16 % (1898973)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=3435468202:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.27/1.16 % (1898977)dis-21_1_sil=8000:lcm=predicate:random_seed=4094759911: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)
% 2.27/1.16 % (1898974)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1790493995:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.27/1.16 % (1898976)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2832080319:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.27/1.16 % (1898974)Also succeeded, but the first one will report.
% 2.27/1.16 % (1898977)Instruction limit reached!
% 2.27/1.16 % (1898977)------------------------------
% 2.27/1.16 % (1898977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.27/1.16 % (1898977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/1.16 % (1898977)CaDiCaL version: 2.1.3
% 2.27/1.16 % (1898977)Termination reason: Instruction limit
% 2.27/1.16 % (1898977)Termination phase: Saturation
% 2.27/1.16 % (1898977)Time elapsed: 0.067 s
% 2.27/1.16 % (1898977)Peak memory usage: 90 MB
% 2.27/1.16 % (1898977)Instructions burned: 131 (million)
% 2.27/1.16 % (1898976)Also succeeded, but the first one will report.
% 2.27/1.16 % (1898975)Refutation found. Thanks to Tanya!
% 2.27/1.16 % SZS status Theorem for theBenchmark
% 2.27/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.36 % (1898975)------------------------------
% 2.67/1.36 % (1898975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.36 % (1898975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.36 % (1898975)CaDiCaL version: 2.1.3
% 2.67/1.36 % (1898975)Termination reason: Refutation
% 2.67/1.36 % (1898975)Time elapsed: 0.007 s
% 2.67/1.36 % (1898975)Peak memory usage: 88 MB
% 2.67/1.36 % (1898975)Instructions burned: 17 (million)
% 2.67/1.36 % (1898975)------------------------------
% 2.67/1.36 % (1898975)------------------------------
% 2.67/1.36 % (1898966)Success in time 0.288 s
% 2.67/1.36 % Vampire exiting
%------------------------------------------------------------------------------