%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU411+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:57:24 PM UTC 2026
% Result : Theorem 3.73s 1.28s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 109 ( 41 unt; 4 def)
% Number of atoms : 522 ( 24 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 576 ( 213 ~; 194 |; 142 &)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 6 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 179 ( 0 sgn 167 !; 12 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_orders_2(X0)
& v1_lattice3(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_orders_2(X1)
& v1_lattice3(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& v1_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_orders_2(X0)
& v1_lattice3(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_orders_2(X1)
& v1_lattice3(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& v1_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
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))
=> ( ( r1_orders_2(X0,X3,X2)
& r2_hidden(X2,X1) )
=> r2_hidden(X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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,X1)
& r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
fof(f18,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f33,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f35,axiom,
! [X0] :
( ( l1_orders_2(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r1_orders_2(X0,k3_yellow_0(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f45,plain,
~ ! [X0] :
( ( l1_orders_2(X0)
& v1_lattice3(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_orders_2(X1)
& v1_lattice3(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
inference(pure_predicate_removal,[],[f2]) ).
fof(f46,plain,
~ ! [X0] :
( ( l1_orders_2(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ( ( m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1))) )
=> r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ) ),
inference(pure_predicate_removal,[],[f45]) ).
fof(f47,plain,
? [X0] :
( l1_orders_2(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f48,plain,
? [X0] :
( l1_orders_2(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)))
& ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(X0)) ) ),
inference(flattening,[],[f47]) ).
fof(f50,plain,
! [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))
| ~ r1_orders_2(X0,X3,X2)
| ~ r2_hidden(X2,X1)
| r2_hidden(X3,X1) ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [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))
| ~ r1_orders_2(X0,X3,X2)
| ~ r2_hidden(X2,X1)
| r2_hidden(X3,X1) ) ) ) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ l1_orders_2(X0)
| m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f67,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f68,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f67]) ).
fof(f70,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| r1_orders_2(X0,k3_yellow_0(X0),X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| r1_orders_2(X0,k3_yellow_0(X0),X1) ) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(flattening,[],[f72]) ).
fof(f78,plain,
( l1_orders_2(sK0)
& v1_yellow_0(sK0)
& v4_orders_2(sK0)
& v3_orders_2(sK0)
& v2_orders_2(sK0)
& ~ v3_struct_0(sK0)
& l1_orders_2(sK1)
& v1_yellow_0(sK1)
& v4_orders_2(sK1)
& v3_orders_2(sK1)
& v2_orders_2(sK1)
& ~ v3_struct_0(sK1)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
& ~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f48]) ).
fof(f79,plain,
! [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))
| ~ r1_orders_2(X0,X3,X2)
| ~ r2_hidden(X2,X1)
| r2_hidden(X3,X1) ) ) )
& ( ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& r1_orders_2(X0,X3,X2)
& r2_hidden(X2,X1)
& ~ r2_hidden(X3,X1) ) )
| v12_waybel_0(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f80,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( ( ~ v12_waybel_0(X1,X0)
| ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(X0))
| ! [X5] :
( ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ r1_orders_2(X0,X5,X4)
| ~ r2_hidden(X4,X1)
| r2_hidden(X5,X1) ) ) )
& ( ? [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
& ? [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
& r1_orders_2(X0,X3,X2)
& r2_hidden(X2,X1)
& ~ r2_hidden(X3,X1) ) )
| v12_waybel_0(X1,X0) ) ) ) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ l1_orders_2(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( ( ~ v12_waybel_0(X1,X0)
| ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(X0))
| ! [X5] :
( ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ r1_orders_2(X0,X5,X4)
| ~ r2_hidden(X4,X1)
| r2_hidden(X5,X1) ) ) )
& ( ( m1_subset_1(sK2(X0,X1),u1_struct_0(X0))
& m1_subset_1(sK3(X0,X1),u1_struct_0(X0))
& r1_orders_2(X0,sK3(X0,X1),sK2(X0,X1))
& r2_hidden(sK2(X0,X1),X1)
& ~ r2_hidden(sK3(X0,X1),X1) )
| v12_waybel_0(X1,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f80]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X0) ) )
& ( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X0) ) )
& ( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ) ) )
& ( ( ( r2_hidden(sK5(X0,X1,X2),X2)
| ( r2_hidden(sK5(X0,X1,X2),X1)
& r2_hidden(sK5(X0,X1,X2),X0) ) )
& ( ~ r2_hidden(sK5(X0,X1,X2),X2)
| ~ r2_hidden(sK5(X0,X1,X2),X1)
| ~ r2_hidden(sK5(X0,X1,X2),X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f87]) ).
fof(f91,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f18]) ).
fof(f104,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f105,plain,
v1_yellow_0(sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f106,plain,
v4_orders_2(sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f110,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,[],[f78]) ).
fof(f111,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f115,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f116,plain,
! [X0,X1,X4,X5] :
( ~ l1_orders_2(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v12_waybel_0(X1,X0)
| ~ m1_subset_1(X4,u1_struct_0(X0))
| ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ r1_orders_2(X0,X5,X4)
| ~ r2_hidden(X4,X1)
| r2_hidden(X5,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f124,plain,
! [X2,X0,X1,X4] :
( k3_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( k3_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f126,plain,
! [X2,X0,X1,X4] :
( k3_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f130,plain,
! [X0] :
( ~ l1_orders_2(X0)
| m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f134,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f91]) ).
fof(f154,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f156,plain,
! [X0,X1] :
( ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| r1_orders_2(X0,k3_yellow_0(X0),X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f163,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,k3_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f126]) ).
fof(f164,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k3_xboole_0(X0,X1))
| r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f165,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,k3_xboole_0(X0,X1))
| r2_hidden(X4,X1) ),
inference(equality_resolution,[],[f124]) ).
tcf(c_49,negated_conjecture,
~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0)),
inference(cnf_transformation,[],[f113]) ).
tcf(c_50,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),
inference(cnf_transformation,[],[f112]) ).
tcf(c_51,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f111]) ).
tcf(c_52,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f110]) ).
tcf(c_53,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f109]) ).
tcf(c_56,negated_conjecture,
v4_orders_2(sK1),
inference(cnf_transformation,[],[f106]) ).
tcf(c_57,negated_conjecture,
v1_yellow_0(sK1),
inference(cnf_transformation,[],[f105]) ).
tcf(c_58,negated_conjecture,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f104]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f115]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X2,X0)
| ~ l1_orders_2(X1)
| ~ v12_waybel_0(X0,X1)
| ~ r2_hidden(X3,X0)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r1_orders_2(X1,X2,X3)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,k3_xboole_0(X2,X1))
| ~ r2_hidden(X0,X2)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X1)
| ~ r2_hidden(X0,k3_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,X2)
| ~ r2_hidden(X0,k3_xboole_0(X1,X2)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_81,plain,
! [X0: $i] :
( m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_85,plain,
! [X0: $i] : m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f134]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| r1_orders_2(X1,k3_yellow_0(X1),X0)
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X2,X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_123,plain,
( m1_subset_1(k3_yellow_0(sK1),u1_struct_0(sK1))
| ~ l1_orders_2(sK1) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X2,X0)
| ~ l1_orders_2(X1)
| ~ v12_waybel_0(X0,X1)
| ~ r2_hidden(X3,X0)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r1_orders_2(X1,X2,X3)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_72,c_108]) ).
tcf(c_486,plain,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0))),
inference(demodulation,[status(thm)],[c_50,c_66]) ).
tcf(c_487,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)),sK1),
inference(demodulation,[status(thm)],[c_51,c_66]) ).
tcf(c_518,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(demodulation,[status(thm)],[c_52,c_66]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| r1_orders_2(X0,k3_yellow_0(X0),X1)
| ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_107]) ).
tcf(c_744,plain,
! [X0: $i] :
( v3_struct_0(sK1)
| r1_orders_2(sK1,k3_yellow_0(sK1),X0)
| ~ l1_orders_2(sK1)
| ~ v1_yellow_0(sK1)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(unflattening,[status(thm)],[c_743]) ).
tcf(c_746,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| r1_orders_2(sK1,k3_yellow_0(sK1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_744,c_58,c_57,c_53,c_744]) ).
tcf(c_747,plain,
! [X0: $i] :
( r1_orders_2(sK1,k3_yellow_0(sK1),X0)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(renaming,[status(thm)],[c_746]) ).
tcf(c_1009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( r2_hidden(X1,X4)
| ~ l1_orders_2(X0)
| ~ v12_waybel_0(X4,X0)
| ~ r2_hidden(X2,X4)
| ~ m1_subset_1(X3,u1_struct_0(sK1))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X0)))
| ( X2 != X3 )
| ( X0 != sK1 )
| ( k3_yellow_0(sK1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_279,c_747]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k3_yellow_0(sK1),X0)
| ~ l1_orders_2(sK1)
| ~ v12_waybel_0(X0,sK1)
| ~ r2_hidden(X1,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ m1_subset_1(k3_yellow_0(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(unflattening,[status(thm)],[c_1009]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k3_yellow_0(sK1),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ r2_hidden(X1,X0)
| ~ v12_waybel_0(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_1010,c_58,c_123,c_1010]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k3_yellow_0(sK1),X0)
| ~ v12_waybel_0(X0,sK1)
| ~ r2_hidden(X1,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(renaming,[status(thm)],[c_1011]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i] :
( r2_hidden(k3_yellow_0(sK1),X0)
| ~ v12_waybel_0(X0,sK1)
| ~ r2_hidden(X1,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1012,c_108]) ).
tcf(c_1518,definition,
iPr_def_13 = u1_struct_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1519,definition,
iPr_def_14 = k1_zfmisc_1(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1520,definition,
iPr_def_15 = k3_yellow_0(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1523,definition,
iPr_def_18 = k3_xboole_0(iPr_def_13,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_1525,plain,
! [X0: $i,X1: $i] :
( r2_hidden(iPr_def_15,X1)
| ~ m1_subset_1(X1,iPr_def_14)
| ~ v12_waybel_0(X1,sK1)
| ~ r2_hidden(X0,X1) ),
inference(demodulation,[status(thm)],[c_1023,c_1520,c_1518,c_1519]) ).
tcf(c_1532,plain,
m1_subset_1(iPr_def_18,iPr_def_14),
inference(demodulation,[status(thm)],[c_518,c_1523]) ).
tcf(c_1533,plain,
v12_waybel_0(iPr_def_18,sK1),
inference(demodulation,[status(thm)],[c_487]) ).
tcf(c_1534,plain,
~ v1_xboole_0(iPr_def_18),
inference(demodulation,[status(thm)],[c_486]) ).
tcf(c_1539,negated_conjecture,
~ r2_hidden(iPr_def_15,iPr_def_10),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_2405,plain,
k3_xboole_0(iPr_def_10,iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_1523,c_66]) ).
tcf(c_2540,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_10)
| ~ r2_hidden(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_2405,c_79]) ).
tcf(c_2557,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_2405,c_80]) ).
tcf(c_2570,plain,
! [X0: $i] :
( v1_xboole_0(X0)
| r2_hidden(sK8(X0),X0) ),
inference(superposition,[status(thm)],[c_85,c_105]) ).
tcf(c_2789,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_18)
| ~ r2_hidden(X0,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2405,c_78]) ).
tcf(c_2931,plain,
( v1_xboole_0(iPr_def_18)
| r2_hidden(sK8(iPr_def_18),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2570,c_2540]) ).
tcf(c_2932,plain,
r2_hidden(sK8(iPr_def_18),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2931,c_1534]) ).
tcf(c_3651,plain,
( v1_xboole_0(iPr_def_18)
| r2_hidden(sK8(iPr_def_18),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2570,c_2557]) ).
tcf(c_3652,plain,
r2_hidden(sK8(iPr_def_18),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_3651,c_1534]) ).
tcf(c_11146,plain,
( r2_hidden(sK8(iPr_def_18),iPr_def_18)
| ~ r2_hidden(sK8(iPr_def_18),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2932,c_2789]) ).
tcf(c_11164,plain,
r2_hidden(sK8(iPr_def_18),iPr_def_18),
inference(forward_subsumption_resolution,[status(thm)],[c_11146,c_3652]) ).
tcf(c_11419,plain,
( r2_hidden(iPr_def_15,iPr_def_18)
| ~ m1_subset_1(iPr_def_18,iPr_def_14)
| ~ v12_waybel_0(iPr_def_18,sK1) ),
inference(superposition,[status(thm)],[c_11164,c_1525]) ).
tcf(c_11424,plain,
r2_hidden(iPr_def_15,iPr_def_18),
inference(forward_subsumption_resolution,[status(thm)],[c_11419,c_1532,c_1533]) ).
tcf(c_11438,plain,
r2_hidden(iPr_def_15,iPr_def_10),
inference(superposition,[status(thm)],[c_11424,c_2540]) ).
tcf(c_11439,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11438,c_1539]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU411+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 14:06:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.73/1.28 % SZS status Started for theBenchmark.p
% 3.73/1.28 % SZS status Theorem for theBenchmark.p
% 3.73/1.28
% 3.73/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.73/1.28
% 3.73/1.28 % ------ iProver source info
% 3.73/1.28
% 3.73/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.73/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.73/1.28 % git: non_committed_changes: false
% 3.73/1.28
% 3.73/1.28 % ------ Parsing...
% 3.73/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.73/1.28
% 3.73/1.28 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 3.73/1.28
% 3.73/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.73/1.28
% 3.73/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.73/1.28 % ------ Proving...
% 3.73/1.28 % ------ Problem Properties
% 3.73/1.28
% 3.73/1.28 %
% 3.73/1.28 % clauses 67
% 3.73/1.28 % conjectures 5
% 3.73/1.28 % EPR 28
% 3.73/1.28 % Horn 56
% 3.73/1.28 % unary 37
% 3.73/1.28 % binary 11
% 3.73/1.28 % lits 131
% 3.73/1.28 % lits eq 18
% 3.73/1.28 % fd_pure 0
% 3.73/1.28 % fd_pseudo 0
% 3.73/1.28 % fd_cond 2
% 3.73/1.28 % fd_pseudo_cond 4
% 3.73/1.28 % AC symbols 0
% 3.73/1.28
% 3.73/1.28 % ------ Schedule dynamic 5 is on
% 3.73/1.28
% 3.73/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.73/1.28
% 3.73/1.28
% 3.73/1.28 % ------
% 3.73/1.28 % Current options:
% 3.73/1.28 % ------
% 3.73/1.28
% 3.73/1.28
% 3.73/1.28 %
% 3.73/1.28
% 3.73/1.28 % ------ Proving...
% 3.73/1.28 %
% 3.73/1.28
% 3.73/1.28 % SZS status Theorem for theBenchmark.p
% 3.73/1.28
% 3.73/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.73/1.28
% 3.73/1.28
%------------------------------------------------------------------------------