TSTP Solution File: SEU411+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU411+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:06:08 EDT 2024
% Result : Theorem 3.28s 1.11s
% Output : CNFRefutation 3.28s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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/sandbox/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,[],[f1]) ).
fof(f4,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d19_waybel_0) ).
fof(f7,axiom,
! [X0,X1,X2] :
( k3_xboole_0(X0,X1) = X2
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) ) ),
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)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f44,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,[],[f44]) ).
fof(f47,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(X0))
& 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)))
& l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
& l1_orders_2(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(X0))
& 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)))
& l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
& l1_orders_2(X0)
& v1_yellow_0(X0)
& v4_orders_2(X0)
& v3_orders_2(X0)
& v2_orders_2(X0)
& ~ v3_struct_0(X0) ),
inference(flattening,[],[f47]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( v12_waybel_0(X1,X0)
<=> ! [X2] :
( ! [X3] :
( r2_hidden(X3,X1)
| ~ r1_orders_2(X0,X3,X2)
| ~ r2_hidden(X2,X1)
| ~ 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(f51,plain,
! [X0] :
( ! [X1] :
( ( v12_waybel_0(X1,X0)
<=> ! [X2] :
( ! [X3] :
( r2_hidden(X3,X1)
| ~ r1_orders_2(X0,X3,X2)
| ~ r2_hidden(X2,X1)
| ~ 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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f67,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f68,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f67]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( r1_orders_2(X0,k3_yellow_0(X0),X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( r1_orders_2(X0,k3_yellow_0(X0),X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f73,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(flattening,[],[f72]) ).
fof(f78,plain,
( ? [X0] :
( ? [X1] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(X0))
& 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)))
& l1_orders_2(X1)
& v1_yellow_0(X1)
& v4_orders_2(X1)
& v3_orders_2(X1)
& v2_orders_2(X1)
& ~ v3_struct_0(X1) )
& 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] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(sK0))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(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) )
& l1_orders_2(sK0)
& v1_yellow_0(sK0)
& v4_orders_2(sK0)
& v3_orders_2(sK0)
& v2_orders_2(sK0)
& ~ v3_struct_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
( ? [X1] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(sK0))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(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) )
=> ( ~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0))
& 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)))
& l1_orders_2(sK1)
& v1_yellow_0(sK1)
& v4_orders_2(sK1)
& v3_orders_2(sK1)
& v2_orders_2(sK1)
& ~ v3_struct_0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
( ~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0))
& 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)))
& l1_orders_2(sK1)
& v1_yellow_0(sK1)
& v4_orders_2(sK1)
& v3_orders_2(sK1)
& v2_orders_2(sK1)
& ~ v3_struct_0(sK1)
& l1_orders_2(sK0)
& v1_yellow_0(sK0)
& v4_orders_2(sK0)
& v3_orders_2(sK0)
& v2_orders_2(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f48,f79,f78]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( v12_waybel_0(X1,X0)
| ? [X2] :
( ? [X3] :
( ~ r2_hidden(X3,X1)
& r1_orders_2(X0,X3,X2)
& r2_hidden(X2,X1)
& m1_subset_1(X3,u1_struct_0(X0)) )
& m1_subset_1(X2,u1_struct_0(X0)) ) )
& ( ! [X2] :
( ! [X3] :
( r2_hidden(X3,X1)
| ~ r1_orders_2(X0,X3,X2)
| ~ r2_hidden(X2,X1)
| ~ 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,[],[f51]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( ( v12_waybel_0(X1,X0)
| ? [X2] :
( ? [X3] :
( ~ r2_hidden(X3,X1)
& r1_orders_2(X0,X3,X2)
& r2_hidden(X2,X1)
& m1_subset_1(X3,u1_struct_0(X0)) )
& m1_subset_1(X2,u1_struct_0(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( r2_hidden(X5,X1)
| ~ r1_orders_2(X0,X5,X4)
| ~ r2_hidden(X4,X1)
| ~ 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,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X3,X1)
& r1_orders_2(X0,X3,X2)
& r2_hidden(X2,X1)
& m1_subset_1(X3,u1_struct_0(X0)) )
& m1_subset_1(X2,u1_struct_0(X0)) )
=> ( ? [X3] :
( ~ r2_hidden(X3,X1)
& r1_orders_2(X0,X3,sK2(X0,X1))
& r2_hidden(sK2(X0,X1),X1)
& m1_subset_1(X3,u1_struct_0(X0)) )
& m1_subset_1(sK2(X0,X1),u1_struct_0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X3] :
( ~ r2_hidden(X3,X1)
& r1_orders_2(X0,X3,sK2(X0,X1))
& r2_hidden(sK2(X0,X1),X1)
& m1_subset_1(X3,u1_struct_0(X0)) )
=> ( ~ r2_hidden(sK3(X0,X1),X1)
& r1_orders_2(X0,sK3(X0,X1),sK2(X0,X1))
& r2_hidden(sK2(X0,X1),X1)
& m1_subset_1(sK3(X0,X1),u1_struct_0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( v12_waybel_0(X1,X0)
| ( ~ r2_hidden(sK3(X0,X1),X1)
& r1_orders_2(X0,sK3(X0,X1),sK2(X0,X1))
& r2_hidden(sK2(X0,X1),X1)
& m1_subset_1(sK3(X0,X1),u1_struct_0(X0))
& m1_subset_1(sK2(X0,X1),u1_struct_0(X0)) ) )
& ( ! [X4] :
( ! [X5] :
( r2_hidden(X5,X1)
| ~ r1_orders_2(X0,X5,X4)
| ~ r2_hidden(X4,X1)
| ~ 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(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f82,f84,f83]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = X2
| ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( 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,X1)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = X2
| ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( 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,X1)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = X2
| ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,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) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,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) )
| r2_hidden(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = 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) )
| r2_hidden(sK5(X0,X1,X2),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) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f92,f93]) ).
fof(f99,plain,
! [X0] :
( ? [X1] : m1_subset_1(X1,X0)
=> m1_subset_1(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f18,f99]) ).
fof(f118,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
v4_orders_2(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
v1_yellow_0(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),
inference(cnf_transformation,[],[f80]) ).
fof(f125,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f126,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,[],[f80]) ).
fof(f127,plain,
~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0)),
inference(cnf_transformation,[],[f80]) ).
fof(f129,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f130,plain,
! [X0,X1,X4,X5] :
( r2_hidden(X5,X1)
| ~ r1_orders_2(X0,X5,X4)
| ~ r2_hidden(X4,X1)
| ~ 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,[],[f85]) ).
fof(f138,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X0)
| ~ r2_hidden(X4,X2)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f144,plain,
! [X0] :
( m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f148,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f100]) ).
fof(f168,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f170,plain,
! [X0,X1] :
( r1_orders_2(X0,k3_yellow_0(X0),X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f171,plain,
! [X2,X0,X1] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f179,plain,
! [X0,X1,X4] :
( r2_hidden(X4,X0)
| ~ r2_hidden(X4,k3_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f138]) ).
cnf(c_49,negated_conjecture,
~ r2_hidden(k3_yellow_0(sK1),u1_struct_0(sK0)),
inference(cnf_transformation,[],[f127]) ).
cnf(c_50,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,[],[f126]) ).
cnf(c_51,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f125]) ).
cnf(c_52,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),
inference(cnf_transformation,[],[f124]) ).
cnf(c_53,negated_conjecture,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f123]) ).
cnf(c_54,negated_conjecture,
v1_yellow_0(sK1),
inference(cnf_transformation,[],[f122]) ).
cnf(c_55,negated_conjecture,
v4_orders_2(sK1),
inference(cnf_transformation,[],[f121]) ).
cnf(c_58,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f118]) ).
cnf(c_66,plain,
k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f129]) ).
cnf(c_72,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_orders_2(X1,X2,X3)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r2_hidden(X3,X0)
| ~ v12_waybel_0(X0,X1)
| ~ l1_orders_2(X1)
| r2_hidden(X2,X0) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_80,plain,
( ~ r2_hidden(X0,k3_xboole_0(X1,X2))
| r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
cnf(c_81,plain,
( ~ l1_orders_2(X0)
| m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_85,plain,
m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f148]) ).
cnf(c_105,plain,
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_107,plain,
( ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| r1_orders_2(X1,k3_yellow_0(X1),X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_108,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r2_hidden(X2,X0)
| m1_subset_1(X2,X1) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_123,plain,
( ~ l1_orders_2(sK1)
| m1_subset_1(k3_yellow_0(sK1),u1_struct_0(sK1)) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_279,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_orders_2(X1,X2,X3)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X3,X0)
| ~ v12_waybel_0(X0,X1)
| ~ l1_orders_2(X1)
| r2_hidden(X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_72,c_108]) ).
cnf(c_486,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0)),sK1),
inference(demodulation,[status(thm)],[c_51,c_66]) ).
cnf(c_487,plain,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK1),u1_struct_0(sK0))),
inference(demodulation,[status(thm)],[c_52,c_66]) ).
cnf(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_50,c_66]) ).
cnf(c_743,plain,
( X0 != sK1
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ v4_orders_2(X0)
| r1_orders_2(X0,k3_yellow_0(X0),X1)
| v3_struct_0(X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_107]) ).
cnf(c_744,plain,
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ l1_orders_2(sK1)
| ~ v4_orders_2(sK1)
| r1_orders_2(sK1,k3_yellow_0(sK1),X0)
| v3_struct_0(sK1) ),
inference(unflattening,[status(thm)],[c_743]) ).
cnf(c_746,plain,
( r1_orders_2(sK1,k3_yellow_0(sK1),X0)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_744,c_55,c_53,c_58,c_744]) ).
cnf(c_747,plain,
( ~ m1_subset_1(X0,u1_struct_0(sK1))
| r1_orders_2(sK1,k3_yellow_0(sK1),X0) ),
inference(renaming,[status(thm)],[c_746]) ).
cnf(c_1009,plain,
( k3_yellow_0(sK1) != X1
| X0 != sK1
| X2 != X3
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(sK1))
| ~ r2_hidden(X2,X4)
| ~ v12_waybel_0(X4,X0)
| ~ l1_orders_2(X0)
| r2_hidden(X1,X4) ),
inference(resolution_lifted,[status(thm)],[c_279,c_747]) ).
cnf(c_1010,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ m1_subset_1(k3_yellow_0(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(X1,u1_struct_0(sK1))
| ~ r2_hidden(X1,X0)
| ~ v12_waybel_0(X0,sK1)
| ~ l1_orders_2(sK1)
| r2_hidden(k3_yellow_0(sK1),X0) ),
inference(unflattening,[status(thm)],[c_1009]) ).
cnf(c_1011,plain,
( ~ 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)))
| r2_hidden(k3_yellow_0(sK1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_1010,c_53,c_123,c_1010]) ).
cnf(c_1012,plain,
( ~ 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)
| r2_hidden(k3_yellow_0(sK1),X0) ),
inference(renaming,[status(thm)],[c_1011]) ).
cnf(c_1023,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r2_hidden(X1,X0)
| ~ v12_waybel_0(X0,sK1)
| r2_hidden(k3_yellow_0(sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1012,c_108]) ).
cnf(c_1515,plain,
k3_yellow_0(sK1) = sP0_iProver_def,
definition ).
cnf(c_1516,plain,
u1_struct_0(sK0) = sP1_iProver_def,
definition ).
cnf(c_1521,negated_conjecture,
~ r2_hidden(sP0_iProver_def,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_49,c_1516,c_1515]) ).
cnf(c_2219,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK1),sP1_iProver_def),sK1),
inference(light_normalisation,[status(thm)],[c_486,c_1516]) ).
cnf(c_2220,plain,
v12_waybel_0(k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1)),sK1),
inference(demodulation,[status(thm)],[c_2219,c_66]) ).
cnf(c_2221,plain,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK1),sP1_iProver_def)),
inference(light_normalisation,[status(thm)],[c_487,c_1516]) ).
cnf(c_2222,plain,
~ v1_xboole_0(k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1))),
inference(demodulation,[status(thm)],[c_2221,c_66]) ).
cnf(c_2223,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK1),sP1_iProver_def),k1_zfmisc_1(u1_struct_0(sK1))),
inference(light_normalisation,[status(thm)],[c_518,c_1516]) ).
cnf(c_2224,plain,
m1_subset_1(k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(demodulation,[status(thm)],[c_2223,c_66]) ).
cnf(c_2226,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ r2_hidden(X1,X0)
| ~ v12_waybel_0(X0,sK1)
| r2_hidden(sP0_iProver_def,X0) ),
inference(light_normalisation,[status(thm)],[c_1023,c_1515]) ).
cnf(c_2238,plain,
( ~ r2_hidden(X0,k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1)))
| ~ v12_waybel_0(k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1)),sK1)
| r2_hidden(sP0_iProver_def,k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_2224,c_2226]) ).
cnf(c_2245,plain,
( ~ r2_hidden(X0,k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1)))
| r2_hidden(sP0_iProver_def,k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2238,c_2220]) ).
cnf(c_2601,plain,
( r2_hidden(sK8(X0),X0)
| v1_xboole_0(X0) ),
inference(superposition,[status(thm)],[c_85,c_105]) ).
cnf(c_2643,plain,
( r2_hidden(sP0_iProver_def,k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1)))
| v1_xboole_0(k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1))) ),
inference(superposition,[status(thm)],[c_2601,c_2245]) ).
cnf(c_2651,plain,
r2_hidden(sP0_iProver_def,k3_xboole_0(sP1_iProver_def,u1_struct_0(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_2643,c_2222]) ).
cnf(c_3261,plain,
r2_hidden(sP0_iProver_def,sP1_iProver_def),
inference(superposition,[status(thm)],[c_2651,c_80]) ).
cnf(c_3263,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3261,c_1521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU411+1 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.31 % Computer : n028.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Thu May 2 18:07:03 EDT 2024
% 0.12/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.28/1.11 % SZS status Started for theBenchmark.p
% 3.28/1.11 % SZS status Theorem for theBenchmark.p
% 3.28/1.11
% 3.28/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.28/1.11
% 3.28/1.11 ------ iProver source info
% 3.28/1.11
% 3.28/1.11 git: date: 2024-05-02 19:28:25 +0000
% 3.28/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.28/1.11 git: non_committed_changes: false
% 3.28/1.11
% 3.28/1.11 ------ Parsing...
% 3.28/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.28/1.11
% 3.28/1.11 ------ 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
% 3.28/1.11
% 3.28/1.11 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.28/1.11
% 3.28/1.11 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.28/1.11 ------ Proving...
% 3.28/1.11 ------ Problem Properties
% 3.28/1.11
% 3.28/1.11
% 3.28/1.11 clauses 60
% 3.28/1.11 conjectures 5
% 3.28/1.11 EPR 17
% 3.28/1.11 Horn 49
% 3.28/1.11 unary 30
% 3.28/1.11 binary 11
% 3.28/1.11 lits 124
% 3.28/1.12 lits eq 11
% 3.28/1.12 fd_pure 0
% 3.28/1.12 fd_pseudo 0
% 3.28/1.12 fd_cond 2
% 3.28/1.12 fd_pseudo_cond 4
% 3.28/1.12 AC symbols 0
% 3.28/1.12
% 3.28/1.12 ------ Schedule dynamic 5 is on
% 3.28/1.12
% 3.28/1.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.28/1.12
% 3.28/1.12
% 3.28/1.12 ------
% 3.28/1.12 Current options:
% 3.28/1.12 ------
% 3.28/1.12
% 3.28/1.12
% 3.28/1.12
% 3.28/1.12
% 3.28/1.12 ------ Proving...
% 3.28/1.12
% 3.28/1.12
% 3.28/1.12 % SZS status Theorem for theBenchmark.p
% 3.28/1.12
% 3.28/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.28/1.12
% 3.28/1.12
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