TSTP Solution File: SEU411+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU411+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 : Sun May 5 09:39:10 EDT 2024
% Result : Theorem 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 92 ( 21 unt; 0 def)
% Number of atoms : 522 ( 8 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 635 ( 205 ~; 181 |; 211 &)
% ( 10 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 184 ( 162 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3744,plain,
$false,
inference(subsumption_resolution,[],[f3733,f134]) ).
fof(f134,plain,
~ r2_hidden(k3_yellow_0(sK4),u1_struct_0(sK3)),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( ~ r2_hidden(k3_yellow_0(sK4),u1_struct_0(sK3))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),k1_zfmisc_1(u1_struct_0(sK4)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
& l1_orders_2(sK4)
& v1_yellow_0(sK4)
& v4_orders_2(sK4)
& v3_orders_2(sK4)
& v2_orders_2(sK4)
& ~ v3_struct_0(sK4)
& l1_orders_2(sK3)
& v1_yellow_0(sK3)
& v4_orders_2(sK3)
& v3_orders_2(sK3)
& v2_orders_2(sK3)
& ~ v3_struct_0(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f48,f84,f83]) ).
fof(f83,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(sK3))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),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(sK3)
& v1_yellow_0(sK3)
& v4_orders_2(sK3)
& v3_orders_2(sK3)
& v2_orders_2(sK3)
& ~ v3_struct_0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ? [X1] :
( ~ r2_hidden(k3_yellow_0(X1),u1_struct_0(sK3))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(X1)),X1)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),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(sK4),u1_struct_0(sK3))
& m1_subset_1(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),k1_zfmisc_1(u1_struct_0(sK4)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
& l1_orders_2(sK4)
& v1_yellow_0(sK4)
& v4_orders_2(sK4)
& v3_orders_2(sK4)
& v2_orders_2(sK4)
& ~ v3_struct_0(sK4) ) ),
introduced(choice_axiom,[]) ).
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(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(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(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(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(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(f3733,plain,
r2_hidden(k3_yellow_0(sK4),u1_struct_0(sK3)),
inference(resolution,[],[f3727,f309]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ r2_hidden(X0,k3_xboole_0(X1,X2))
| r2_hidden(X0,X1) ),
inference(resolution,[],[f173,f189]) ).
fof(f189,plain,
! [X0,X1] : sP2(X1,X0,k3_xboole_0(X0,X1)),
inference(equality_resolution,[],[f179]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = X2
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| k3_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( k3_xboole_0(X0,X1) = X2
<=> sP2(X1,X0,X2) ),
inference(definition_folding,[],[f7,f81]) ).
fof(f81,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
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(f173,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ r2_hidden(sK11(X0,X1,X2),X0)
| ~ r2_hidden(sK11(X0,X1,X2),X1)
| ~ r2_hidden(sK11(X0,X1,X2),X2) )
& ( ( r2_hidden(sK11(X0,X1,X2),X0)
& r2_hidden(sK11(X0,X1,X2),X1) )
| r2_hidden(sK11(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) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f105,f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ? [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) ) )
=> ( ( ~ r2_hidden(sK11(X0,X1,X2),X0)
| ~ r2_hidden(sK11(X0,X1,X2),X1)
| ~ r2_hidden(sK11(X0,X1,X2),X2) )
& ( ( r2_hidden(sK11(X0,X1,X2),X0)
& r2_hidden(sK11(X0,X1,X2),X1) )
| r2_hidden(sK11(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [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) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,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) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,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) ) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f3727,plain,
r2_hidden(k3_yellow_0(sK4),k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),
inference(subsumption_resolution,[],[f3726,f131]) ).
fof(f131,plain,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),
inference(cnf_transformation,[],[f85]) ).
fof(f3726,plain,
( r2_hidden(k3_yellow_0(sK4),k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
| v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))) ),
inference(subsumption_resolution,[],[f3716,f272]) ).
fof(f272,plain,
sP0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4),
inference(subsumption_resolution,[],[f271,f132]) ).
fof(f132,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f271,plain,
( ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4)
| sP0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4) ),
inference(resolution,[],[f267,f139]) ).
fof(f139,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ~ v12_waybel_0(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ( ( v12_waybel_0(X1,X0)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ v12_waybel_0(X1,X0) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( v12_waybel_0(X1,X0)
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f267,plain,
sP1(sK4,k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),
inference(subsumption_resolution,[],[f263,f130]) ).
fof(f130,plain,
l1_orders_2(sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f263,plain,
( sP1(sK4,k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
| ~ l1_orders_2(sK4) ),
inference(resolution,[],[f147,f133]) ).
fof(f133,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),k1_zfmisc_1(u1_struct_0(sK4))),
inference(cnf_transformation,[],[f85]) ).
fof(f147,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| sP1(X0,X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( sP1(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_orders_2(X0) ),
inference(definition_folding,[],[f52,f79,f78]) ).
fof(f78,plain,
! [X1,X0] :
( sP0(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)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f52,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,[],[f51]) ).
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(ennf_transformation,[],[f5]) ).
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(f3716,plain,
( r2_hidden(k3_yellow_0(sK4),k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
| ~ sP0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)),sK4)
| v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))) ),
inference(resolution,[],[f3627,f1632]) ).
fof(f1632,plain,
! [X0] :
( r2_hidden(sK10(X0),X0)
| v1_xboole_0(X0) ),
inference(forward_demodulation,[],[f1626,f161]) ).
fof(f161,plain,
! [X0] : k3_xboole_0(X0,X0) = X0,
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] : k3_xboole_0(X0,X0) = X0,
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] : k3_xboole_0(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f1626,plain,
! [X0] :
( r2_hidden(sK10(X0),X0)
| v1_xboole_0(k3_xboole_0(X0,X0)) ),
inference(superposition,[],[f1580,f161]) ).
fof(f1580,plain,
! [X0,X1] :
( r2_hidden(sK10(k3_xboole_0(X0,X1)),X0)
| v1_xboole_0(k3_xboole_0(X0,X1)) ),
inference(resolution,[],[f316,f159]) ).
fof(f159,plain,
! [X0] : m1_subset_1(sK10(X0),X0),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] : m1_subset_1(sK10(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f18,f100]) ).
fof(f100,plain,
! [X0] :
( ? [X1] : m1_subset_1(X1,X0)
=> m1_subset_1(sK10(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f316,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X0,k3_xboole_0(X1,X2))
| v1_xboole_0(k3_xboole_0(X1,X2))
| r2_hidden(X0,X1) ),
inference(resolution,[],[f309,f165]) ).
fof(f165,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
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(f3627,plain,
! [X0] :
( ~ r2_hidden(sK10(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),X0)
| r2_hidden(k3_yellow_0(sK4),X0)
| ~ sP0(X0,sK4) ),
inference(subsumption_resolution,[],[f3626,f125]) ).
fof(f125,plain,
~ v3_struct_0(sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f3626,plain,
! [X0] :
( ~ r2_hidden(sK10(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),X0)
| r2_hidden(k3_yellow_0(sK4),X0)
| ~ sP0(X0,sK4)
| v3_struct_0(sK4) ),
inference(subsumption_resolution,[],[f3625,f128]) ).
fof(f128,plain,
v4_orders_2(sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f3625,plain,
! [X0] :
( ~ r2_hidden(sK10(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),X0)
| r2_hidden(k3_yellow_0(sK4),X0)
| ~ sP0(X0,sK4)
| ~ v4_orders_2(sK4)
| v3_struct_0(sK4) ),
inference(subsumption_resolution,[],[f3624,f129]) ).
fof(f129,plain,
v1_yellow_0(sK4),
inference(cnf_transformation,[],[f85]) ).
fof(f3624,plain,
! [X0] :
( ~ r2_hidden(sK10(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),X0)
| r2_hidden(k3_yellow_0(sK4),X0)
| ~ sP0(X0,sK4)
| ~ v1_yellow_0(sK4)
| ~ v4_orders_2(sK4)
| v3_struct_0(sK4) ),
inference(subsumption_resolution,[],[f3595,f130]) ).
fof(f3595,plain,
! [X0] :
( ~ r2_hidden(sK10(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),X0)
| r2_hidden(k3_yellow_0(sK4),X0)
| ~ sP0(X0,sK4)
| ~ l1_orders_2(sK4)
| ~ v1_yellow_0(sK4)
| ~ v4_orders_2(sK4)
| v3_struct_0(sK4) ),
inference(resolution,[],[f1065,f307]) ).
fof(f307,plain,
m1_subset_1(sK10(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))),u1_struct_0(sK4)),
inference(resolution,[],[f304,f159]) ).
fof(f304,plain,
! [X0] :
( ~ m1_subset_1(X0,k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
| m1_subset_1(X0,u1_struct_0(sK4)) ),
inference(subsumption_resolution,[],[f303,f131]) ).
fof(f303,plain,
! [X0] :
( m1_subset_1(X0,u1_struct_0(sK4))
| v1_xboole_0(k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
| ~ m1_subset_1(X0,k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4))) ),
inference(resolution,[],[f291,f165]) ).
fof(f291,plain,
! [X0] :
( ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK3),u1_struct_0(sK4)))
| m1_subset_1(X0,u1_struct_0(sK4)) ),
inference(resolution,[],[f172,f133]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(flattening,[],[f75]) ).
fof(f75,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(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(f1065,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r2_hidden(X2,X1)
| r2_hidden(k3_yellow_0(X0),X1)
| ~ sP0(X1,X0)
| ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0) ),
inference(subsumption_resolution,[],[f1062,f138]) ).
fof(f138,plain,
! [X0] :
( m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f11]) ).
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(f1062,plain,
! [X2,X0,X1] :
( r2_hidden(k3_yellow_0(X0),X1)
| ~ r2_hidden(X2,X1)
| ~ m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ sP0(X1,X0)
| ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0) ),
inference(duplicate_literal_removal,[],[f1061]) ).
fof(f1061,plain,
! [X2,X0,X1] :
( r2_hidden(k3_yellow_0(X0),X1)
| ~ r2_hidden(X2,X1)
| ~ m1_subset_1(k3_yellow_0(X0),u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ sP0(X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ v1_yellow_0(X0)
| ~ v4_orders_2(X0)
| v3_struct_0(X0) ),
inference(resolution,[],[f141,f149]) ).
fof(f149,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,[],[f55]) ).
fof(f55,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,[],[f54]) ).
fof(f54,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(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(f141,plain,
! [X0,X1,X4,X5] :
( ~ r1_orders_2(X1,X5,X4)
| r2_hidden(X5,X0)
| ~ r2_hidden(X4,X0)
| ~ m1_subset_1(X5,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ r2_hidden(sK6(X0,X1),X0)
& r1_orders_2(X1,sK6(X0,X1),sK5(X0,X1))
& r2_hidden(sK5(X0,X1),X0)
& m1_subset_1(sK6(X0,X1),u1_struct_0(X1))
& m1_subset_1(sK5(X0,X1),u1_struct_0(X1)) ) )
& ( ! [X4] :
( ! [X5] :
( r2_hidden(X5,X0)
| ~ r1_orders_2(X1,X5,X4)
| ~ r2_hidden(X4,X0)
| ~ m1_subset_1(X5,u1_struct_0(X1)) )
| ~ m1_subset_1(X4,u1_struct_0(X1)) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f88,f90,f89]) ).
fof(f89,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X3,X0)
& r1_orders_2(X1,X3,X2)
& r2_hidden(X2,X0)
& m1_subset_1(X3,u1_struct_0(X1)) )
& m1_subset_1(X2,u1_struct_0(X1)) )
=> ( ? [X3] :
( ~ r2_hidden(X3,X0)
& r1_orders_2(X1,X3,sK5(X0,X1))
& r2_hidden(sK5(X0,X1),X0)
& m1_subset_1(X3,u1_struct_0(X1)) )
& m1_subset_1(sK5(X0,X1),u1_struct_0(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X3] :
( ~ r2_hidden(X3,X0)
& r1_orders_2(X1,X3,sK5(X0,X1))
& r2_hidden(sK5(X0,X1),X0)
& m1_subset_1(X3,u1_struct_0(X1)) )
=> ( ~ r2_hidden(sK6(X0,X1),X0)
& r1_orders_2(X1,sK6(X0,X1),sK5(X0,X1))
& r2_hidden(sK5(X0,X1),X0)
& m1_subset_1(sK6(X0,X1),u1_struct_0(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ? [X3] :
( ~ r2_hidden(X3,X0)
& r1_orders_2(X1,X3,X2)
& r2_hidden(X2,X0)
& m1_subset_1(X3,u1_struct_0(X1)) )
& m1_subset_1(X2,u1_struct_0(X1)) ) )
& ( ! [X4] :
( ! [X5] :
( r2_hidden(X5,X0)
| ~ r1_orders_2(X1,X5,X4)
| ~ r2_hidden(X4,X0)
| ~ m1_subset_1(X5,u1_struct_0(X1)) )
| ~ m1_subset_1(X4,u1_struct_0(X1)) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X1,X0] :
( ( sP0(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)) )
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU411+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:27:19 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (24695)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (24698)WARNING: value z3 for option sas not known
% 0.15/0.38 % (24696)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (24697)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (24699)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (24700)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (24701)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (24702)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 % (24698)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.40 TRYING [4]
% 0.22/0.42 TRYING [5]
% 0.22/0.43 TRYING [3]
% 0.22/0.47 TRYING [6]
% 0.22/0.50 TRYING [4]
% 0.22/0.52 % (24698)First to succeed.
% 0.22/0.52 % (24698)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24695"
% 0.22/0.53 % (24702)Also succeeded, but the first one will report.
% 0.22/0.53 % (24698)Refutation found. Thanks to Tanya!
% 0.22/0.53 % SZS status Theorem for theBenchmark
% 0.22/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.53 % (24698)------------------------------
% 0.22/0.53 % (24698)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.53 % (24698)Termination reason: Refutation
% 0.22/0.53
% 0.22/0.53 % (24698)Memory used [KB]: 2286
% 0.22/0.53 % (24698)Time elapsed: 0.146 s
% 0.22/0.53 % (24698)Instructions burned: 263 (million)
% 0.22/0.53 % (24695)Success in time 0.164 s
%------------------------------------------------------------------------------