%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT359+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 11:47:18 AM UTC 2026
% Result : Theorem 3.58s 1.48s
% Output : Refutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 122 ( 22 unt; 3 def)
% Number of atoms : 364 ( 71 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 405 ( 163 ~; 159 |; 52 &)
% ( 13 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 185 ( 0 sgn 177 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& l2_altcat_1(X0) )
=> ! [X1,X2,X3] :
~ ( r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2))
& ! [X4] :
( m1_subset_1(X4,u1_struct_0(X0))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(X0))
=> ~ ( X4 = X1
& X5 = X2
& r2_hidden(X3,k1_altcat_1(X0,X4,X5))
& m1_subset_1(X3,k1_altcat_1(X0,X4,X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_waybel34) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& l2_altcat_1(X0) )
=> ! [X1,X2,X3] :
~ ( r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2))
& ! [X4] :
( m1_subset_1(X4,u1_struct_0(X0))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(X0))
=> ~ ( X4 = X1
& X5 = X2
& r2_hidden(X3,k1_altcat_1(X0,X4,X5))
& m1_subset_1(X3,k1_altcat_1(X0,X4,X5)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f18,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f19,axiom,
! [X0] :
( ( v1_relat_1(X0)
& v1_funct_1(X0) )
=> ! [X1,X2] : k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k4_tarski(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
fof(f20,axiom,
! [X0] :
( l1_altcat_1(X0)
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> k1_altcat_1(X0,X1,X2) = k1_binop_1(u1_altcat_1(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_altcat_1) ).
fof(f21,axiom,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pboole) ).
fof(f22,axiom,
! [X0] :
( ( v1_relat_1(X0)
& v1_funct_1(X0) )
=> ! [X1,X2] :
( ( r2_hidden(X1,k1_relat_1(X0))
=> ( X2 = k1_funct_1(X0,X1)
<=> r2_hidden(k4_tarski(X1,X2),X0) ) )
& ( ~ r2_hidden(X1,k1_relat_1(X0))
=> ( X2 = k1_funct_1(X0,X1)
<=> X2 = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f23,axiom,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f35,axiom,
! [X0] :
( l2_altcat_1(X0)
=> l1_altcat_1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_altcat_1) ).
fof(f36,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( v1_relat_1(X1)
& v1_funct_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
fof(f38,axiom,
! [X0] :
( l1_altcat_1(X0)
=> m1_pboole(u1_altcat_1(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_altcat_1) ).
fof(f58,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(f69,axiom,
! [X0,X1,X2,X3] :
( r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3))
<=> ( r2_hidden(X0,X2)
& r2_hidden(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f70,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f73,axiom,
! [X0,X1] :
~ ( r2_hidden(X0,X1)
& v1_xboole_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f82,plain,
( v1_xboole_0(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
inference(pure_predicate_removal,[],[f58]) ).
fof(f93,plain,
( v1_xboole_0(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
inference(pure_predicate_removal,[],[f82]) ).
fof(f104,plain,
( v1_xboole_0(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
inference(pure_predicate_removal,[],[f93]) ).
fof(f114,plain,
( v1_xboole_0(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
inference(pure_predicate_removal,[],[f104]) ).
fof(f116,plain,
? [X0] :
( ? [X1,X2,X3] :
( r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2))
& ! [X4] :
( ! [X5] :
( X1 != X4
| X2 != X5
| ~ r2_hidden(X3,k1_altcat_1(X0,X4,X5))
| ~ m1_subset_1(X3,k1_altcat_1(X0,X4,X5))
| ~ m1_subset_1(X5,u1_struct_0(X0)) )
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) )
& ~ v3_struct_0(X0)
& l2_altcat_1(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f117,plain,
? [X0] :
( ? [X1,X2,X3] :
( r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2))
& ! [X4] :
( ! [X5] :
( X1 != X4
| X2 != X5
| ~ r2_hidden(X3,k1_altcat_1(X0,X4,X5))
| ~ m1_subset_1(X3,k1_altcat_1(X0,X4,X5))
| ~ m1_subset_1(X5,u1_struct_0(X0)) )
| ~ m1_subset_1(X4,u1_struct_0(X0)) ) )
& ~ v3_struct_0(X0)
& l2_altcat_1(X0) ),
inference(flattening,[],[f116]) ).
fof(f119,plain,
! [X0] :
( m1_pboole(u1_altcat_1(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)))
| ~ l1_altcat_1(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k1_altcat_1(X0,X1,X2) = k1_binop_1(u1_altcat_1(X0),X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_altcat_1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f123,plain,
! [X0] :
( ! [X1,X2] : k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k4_tarski(X1,X2))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f124,plain,
! [X0] :
( ! [X1,X2] : k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k4_tarski(X1,X2))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( l1_altcat_1(X0)
| ~ l2_altcat_1(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f126,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f129,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f130,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = k1_funct_1(X0,X1)
<=> r2_hidden(k4_tarski(X1,X2),X0) )
| ~ r2_hidden(X1,k1_relat_1(X0)) )
& ( ( X2 = k1_funct_1(X0,X1)
<=> X2 = k1_xboole_0 )
| r2_hidden(X1,k1_relat_1(X0)) ) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f131,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = k1_funct_1(X0,X1)
<=> r2_hidden(k4_tarski(X1,X2),X0) )
| ~ r2_hidden(X1,k1_relat_1(X0)) )
& ( ( X2 = k1_funct_1(X0,X1)
<=> X2 = k1_xboole_0 )
| r2_hidden(X1,k1_relat_1(X0)) ) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(flattening,[],[f130]) ).
fof(f136,plain,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f137,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f138,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(flattening,[],[f137]) ).
fof(f150,plain,
( r2_hidden(sK3,k1_binop_1(u1_altcat_1(sK0),sK1,sK2))
& ! [X4] :
( ! [X5] :
( sK1 != X4
| sK2 != X5
| ~ r2_hidden(sK3,k1_altcat_1(sK0,X4,X5))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,X4,X5))
| ~ m1_subset_1(X5,u1_struct_0(sK0)) )
| ~ m1_subset_1(X4,u1_struct_0(sK0)) )
& ~ v3_struct_0(sK0)
& l2_altcat_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f117]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ( r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3))
| ~ r2_hidden(X0,X2)
| ~ r2_hidden(X1,X3) )
& ( ( r2_hidden(X0,X2)
& r2_hidden(X1,X3) )
| ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3)) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( ( r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3))
| ~ r2_hidden(X0,X2)
| ~ r2_hidden(X1,X3) )
& ( ( r2_hidden(X0,X2)
& r2_hidden(X1,X3) )
| ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3)) ) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = k1_funct_1(X0,X1)
| ~ r2_hidden(k4_tarski(X1,X2),X0) )
& ( r2_hidden(k4_tarski(X1,X2),X0)
| k1_funct_1(X0,X1) != X2 ) )
| ~ r2_hidden(X1,k1_relat_1(X0)) )
& ( ( ( X2 = k1_funct_1(X0,X1)
| k1_xboole_0 != X2 )
& ( X2 = k1_xboole_0
| k1_funct_1(X0,X1) != X2 ) )
| r2_hidden(X1,k1_relat_1(X0)) ) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(nnf_transformation,[],[f131]) ).
fof(f159,plain,
! [X0,X1] :
( ( ( m1_pboole(X1,X0)
| k1_relat_1(X1) != X0 )
& ( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0) ) )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(nnf_transformation,[],[f138]) ).
fof(f166,plain,
l2_altcat_1(sK0),
inference(cnf_transformation,[],[f150]) ).
fof(f168,plain,
! [X4,X5] :
( sK1 != X4
| sK2 != X5
| ~ r2_hidden(sK3,k1_altcat_1(sK0,X4,X5))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,X4,X5))
| ~ m1_subset_1(X5,u1_struct_0(sK0))
| ~ m1_subset_1(X4,u1_struct_0(sK0)) ),
inference(cnf_transformation,[],[f150]) ).
fof(f169,plain,
r2_hidden(sK3,k1_binop_1(u1_altcat_1(sK0),sK1,sK2)),
inference(cnf_transformation,[],[f150]) ).
fof(f171,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f18]) ).
fof(f172,plain,
! [X0] :
( m1_pboole(u1_altcat_1(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)))
| ~ l1_altcat_1(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k1_binop_1(u1_altcat_1(X0),X1,X2) = k1_altcat_1(X0,X1,X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_altcat_1(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f177,plain,
! [X2,X0,X1] :
( k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k4_tarski(X1,X2))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f179,plain,
! [X0] :
( ~ l2_altcat_1(X0)
| l1_altcat_1(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f180,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f182,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X1,X3)
| ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,X2)
| ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3)) ),
inference(cnf_transformation,[],[f154]) ).
fof(f186,plain,
! [X2,X0,X1] :
( k1_xboole_0 = X2
| k1_funct_1(X0,X1) != X2
| r2_hidden(X1,k1_relat_1(X0))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f196,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_funct_1(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f197,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_relat_1(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f198,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(cnf_transformation,[],[f159]) ).
fof(f201,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f214,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f114]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))
| ~ v1_funct_1(X0) ),
inference(definition_unfolding,[],[f177,f201]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k2_zfmisc_1(X2,X3))
| r2_hidden(X0,X2) ),
inference(definition_unfolding,[],[f184,f201]) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k2_zfmisc_1(X2,X3))
| r2_hidden(X1,X3) ),
inference(definition_unfolding,[],[f183,f201]) ).
fof(f235,plain,
! [X5] :
( sK2 != X5
| ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,X5))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,sK1,X5))
| ~ m1_subset_1(X5,u1_struct_0(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(equality_resolution,[],[f168]) ).
fof(f236,plain,
( ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(equality_resolution,[],[f235]) ).
fof(f239,plain,
! [X0,X1] :
( r2_hidden(X1,k1_relat_1(X0))
| k1_funct_1(X0,X1) = k1_xboole_0
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(equality_resolution,[],[f186]) ).
fof(f241,plain,
( ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0)) ),
inference(forward_subsumption_resolution,[],[f236,f182]) ).
fof(f243,definition,
( spl15_1
<=> m1_subset_1(sK1,u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f244,plain,
( m1_subset_1(sK1,u1_struct_0(sK0))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( ~ m1_subset_1(sK1,u1_struct_0(sK0))
| spl15_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f247,definition,
( spl15_2
<=> m1_subset_1(sK2,u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f248,plain,
( m1_subset_1(sK2,u1_struct_0(sK0))
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f249,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK0))
| spl15_2 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f251,definition,
( spl15_3
<=> r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f253,plain,
( ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2))
| spl15_3 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f254,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f241,f251,f247,f243]) ).
fof(f255,plain,
l1_altcat_1(sK0),
inference(resolution,[],[f179,f166]) ).
fof(f266,plain,
~ v1_xboole_0(k1_binop_1(u1_altcat_1(sK0),sK1,sK2)),
inference(resolution,[],[f180,f169]) ).
fof(f305,plain,
! [X0] :
( v1_relat_1(u1_altcat_1(X0))
| ~ l1_altcat_1(X0) ),
inference(resolution,[],[f172,f197]) ).
fof(f306,plain,
! [X0] :
( v1_funct_1(u1_altcat_1(X0))
| ~ l1_altcat_1(X0) ),
inference(resolution,[],[f172,f196]) ).
fof(f309,plain,
! [X0] :
( k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)) = k1_relat_1(u1_altcat_1(X0))
| ~ v1_relat_1(u1_altcat_1(X0))
| ~ v1_funct_1(u1_altcat_1(X0))
| ~ l1_altcat_1(X0) ),
inference(resolution,[],[f198,f172]) ).
fof(f311,plain,
! [X0] :
( k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)) = k1_relat_1(u1_altcat_1(X0))
| ~ v1_funct_1(u1_altcat_1(X0))
| ~ l1_altcat_1(X0) ),
inference(forward_subsumption_resolution,[],[f309,f305]) ).
fof(f313,plain,
! [X0] :
( ~ l1_altcat_1(X0)
| k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)) = k1_relat_1(u1_altcat_1(X0)) ),
inference(forward_subsumption_resolution,[],[f311,f306]) ).
fof(f329,plain,
k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)) = k1_relat_1(u1_altcat_1(sK0)),
inference(resolution,[],[f313,f255]) ).
fof(f337,plain,
( m1_pboole(u1_altcat_1(sK0),k1_relat_1(u1_altcat_1(sK0)))
| ~ l1_altcat_1(sK0) ),
inference(superposition,[],[f172,f329]) ).
fof(f338,plain,
! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k1_relat_1(u1_altcat_1(sK0)))
| r2_hidden(X1,u1_struct_0(sK0)) ),
inference(superposition,[],[f232,f329]) ).
fof(f339,plain,
! [X0,X1] :
( ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k1_relat_1(u1_altcat_1(sK0)))
| r2_hidden(X0,u1_struct_0(sK0)) ),
inference(superposition,[],[f231,f329]) ).
fof(f351,plain,
! [X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),k1_relat_1(u1_altcat_1(sK0)))
| r2_hidden(X0,u1_struct_0(sK0)) ),
inference(forward_demodulation,[],[f339,f171]) ).
fof(f352,plain,
! [X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),k1_relat_1(u1_altcat_1(sK0)))
| r2_hidden(X1,u1_struct_0(sK0)) ),
inference(forward_demodulation,[],[f338,f171]) ).
fof(f353,plain,
m1_pboole(u1_altcat_1(sK0),k1_relat_1(u1_altcat_1(sK0))),
inference(forward_subsumption_resolution,[],[f337,f255]) ).
fof(f389,plain,
v1_relat_1(u1_altcat_1(sK0)),
inference(resolution,[],[f353,f197]) ).
fof(f390,plain,
v1_funct_1(u1_altcat_1(sK0)),
inference(resolution,[],[f353,f196]) ).
fof(f401,plain,
! [X0,X1] :
( k1_binop_1(u1_altcat_1(sK0),X0,X1) = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)))
| ~ v1_funct_1(u1_altcat_1(sK0)) ),
inference(resolution,[],[f389,f229]) ).
fof(f402,plain,
! [X0,X1] : k1_binop_1(u1_altcat_1(sK0),X0,X1) = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k2_tarski(X0,X1),k1_tarski(X0))),
inference(forward_subsumption_resolution,[],[f401,f390]) ).
fof(f403,plain,
! [X0,X1] : k1_binop_1(u1_altcat_1(sK0),X0,X1) = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X0),k2_tarski(X0,X1))),
inference(forward_demodulation,[],[f402,f171]) ).
fof(f417,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)))
| ~ v1_relat_1(u1_altcat_1(sK0))
| ~ v1_funct_1(u1_altcat_1(sK0)) ),
inference(resolution,[],[f351,f239]) ).
fof(f420,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)))
| ~ v1_funct_1(u1_altcat_1(sK0)) ),
inference(forward_subsumption_resolution,[],[f417,f389]) ).
fof(f421,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X0),k2_tarski(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f420,f390]) ).
fof(f422,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),X0,X1) ),
inference(forward_demodulation,[],[f421,f403]) ).
fof(f431,plain,
! [X0,X1] :
( m1_subset_1(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),X0,X1) ),
inference(resolution,[],[f422,f182]) ).
fof(f485,plain,
( ! [X0] : k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),sK1,X0)
| spl15_1 ),
inference(resolution,[],[f431,f245]) ).
fof(f511,plain,
( ~ v1_xboole_0(k1_xboole_0)
| spl15_1 ),
inference(superposition,[],[f266,f485]) ).
fof(f513,plain,
( $false
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f511,f214]) ).
fof(f514,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f513]) ).
fof(f553,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X1),k2_tarski(X1,X0)))
| ~ v1_relat_1(u1_altcat_1(sK0))
| ~ v1_funct_1(u1_altcat_1(sK0)) ),
inference(resolution,[],[f352,f239]) ).
fof(f556,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X1),k2_tarski(X1,X0)))
| ~ v1_funct_1(u1_altcat_1(sK0)) ),
inference(forward_subsumption_resolution,[],[f553,f389]) ).
fof(f557,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X1),k2_tarski(X1,X0))) ),
inference(forward_subsumption_resolution,[],[f556,f390]) ).
fof(f558,plain,
! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),X1,X0) ),
inference(forward_demodulation,[],[f557,f403]) ).
fof(f570,plain,
! [X0,X1] :
( m1_subset_1(X1,u1_struct_0(sK0))
| k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),X0,X1) ),
inference(resolution,[],[f558,f182]) ).
fof(f629,plain,
( ! [X0] : k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),X0,sK2)
| spl15_2 ),
inference(resolution,[],[f570,f249]) ).
fof(f646,plain,
( ~ v1_xboole_0(k1_xboole_0)
| spl15_2 ),
inference(superposition,[],[f266,f629]) ).
fof(f648,plain,
( $false
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f646,f214]) ).
fof(f649,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f648]) ).
fof(f653,plain,
( ! [X0] :
( k1_binop_1(u1_altcat_1(sK0),X0,sK2) = k1_altcat_1(sK0,X0,sK2)
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ l1_altcat_1(sK0) )
| ~ spl15_2 ),
inference(resolution,[],[f248,f173]) ).
fof(f657,plain,
( ! [X0] :
( ~ m1_subset_1(X0,u1_struct_0(sK0))
| k1_binop_1(u1_altcat_1(sK0),X0,sK2) = k1_altcat_1(sK0,X0,sK2) )
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f653,f255]) ).
fof(f664,plain,
( k1_binop_1(u1_altcat_1(sK0),sK1,sK2) = k1_altcat_1(sK0,sK1,sK2)
| ~ spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f657,f244]) ).
fof(f679,plain,
( r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ spl15_1
| ~ spl15_2 ),
inference(superposition,[],[f169,f664]) ).
fof(f680,plain,
( $false
| ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f679,f253]) ).
fof(f681,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(avatar_contradiction_clause,[],[f680]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f254]) ).
cnf(s11,plain,
spl15_1,
inference(sat_conversion,[],[f514]) ).
cnf(s16,plain,
spl15_2,
inference(sat_conversion,[],[f649]) ).
cnf(s18,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f681]) ).
cnf(s19,plain,
spl15_3,
inference(rat,[],[s18,s16,s11]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s19,s16,s11]) ).
fof(f682,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT359+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 14:58:10 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.58/1.48 % (1550132)Detected formulas, will run a generic FOF schedule.
% 3.58/1.48 % (1550139)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=1398701050:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/1.48 % (1550141)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=197444512:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/1.48 % (1550141)Refutation not found, incomplete strategy
% 3.58/1.48 % (1550141)------------------------------
% 3.58/1.48 % (1550141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.48 % (1550141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.48 % (1550141)CaDiCaL version: 2.1.3
% 3.58/1.48 % (1550141)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.48 % (1550141)Time elapsed: 0.006 s
% 3.58/1.48 % (1550141)Peak memory usage: 88 MB
% 3.58/1.48 % (1550141)Instructions burned: 7 (million)
% 3.58/1.48 % (1550138)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=510609093:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/1.48 % (1550140)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1962711570:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/1.48 % (1550137)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=2479531135:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/1.48 % (1550140)Refutation not found, incomplete strategy
% 3.58/1.48 % (1550140)------------------------------
% 3.58/1.48 % (1550140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.48 % (1550140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.48 % (1550140)CaDiCaL version: 2.1.3
% 3.58/1.48 % (1550140)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.48 % (1550140)Time elapsed: 0.002 s
% 3.58/1.48 % (1550140)Peak memory usage: 88 MB
% 3.58/1.48 % (1550140)Instructions burned: 2 (million)
% 3.58/1.48 % (1550143)dis-21_1_sil=8000:lcm=predicate:random_seed=2826835089: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)
% 3.58/1.48 % (1550142)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1399598400:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/1.48 % (1550143)Instruction limit reached!
% 3.58/1.48 % (1550143)------------------------------
% 3.58/1.48 % (1550143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.48 % (1550143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.48 % (1550143)CaDiCaL version: 2.1.3
% 3.58/1.48 % (1550143)Termination reason: Instruction limit
% 3.58/1.48 % (1550143)Termination phase: Saturation
% 3.58/1.48 % (1550143)Time elapsed: 0.075 s
% 3.58/1.48 % (1550143)Peak memory usage: 89 MB
% 3.58/1.48 % (1550143)Instructions burned: 129 (million)
% 3.58/1.48 % (1550142)Instruction limit reached!
% 3.58/1.48 % (1550142)------------------------------
% 3.58/1.48 % (1550142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.48 % (1550142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.48 % (1550142)CaDiCaL version: 2.1.3
% 3.58/1.48 % (1550142)Termination reason: Instruction limit
% 3.58/1.48 % (1550142)Termination phase: Saturation
% 3.58/1.48 % (1550142)Time elapsed: 0.091 s
% 3.58/1.48 % (1550142)Peak memory usage: 90 MB
% 3.58/1.48 % (1550142)Instructions burned: 139 (million)
% 3.58/1.48 % (1550151)lrs+10_1_sil=8000:sp=occurrence:random_seed=2702565744:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.58/1.48 % (1550151)First to succeed.
% 3.58/1.48 % (1550151)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1550132"
% 3.58/1.48 % (1550141)------------------------------
% 3.58/1.48 % (1550141)------------------------------
% 3.58/1.48 % (1550152)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1756901226:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.58/1.48 % (1550140)------------------------------
% 3.58/1.48 % (1550140)------------------------------
% 3.58/1.48 % (1550152)Instruction limit reached!
% 3.58/1.48 % (1550152)------------------------------
% 3.58/1.48 % (1550152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.48 % (1550152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.48 % (1550152)CaDiCaL version: 2.1.3
% 3.58/1.48 % (1550152)Termination reason: Instruction limit
% 3.58/1.48 % (1550152)Termination phase: Saturation
% 3.58/1.48 % (1550152)Time elapsed: 0.079 s
% 3.58/1.48 % (1550152)Peak memory usage: 90 MB
% 3.58/1.48 % (1550152)Instructions burned: 157 (million)
% 3.58/1.48 % (1550155)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1908144322:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.58/1.48 % (1550156)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=626005723:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.58/1.48 % (1550157)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2078153844:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.58/1.48 % (1550157)Refutation not found, incomplete strategy
% 3.58/1.48 % (1550157)------------------------------
% 3.58/1.48 % (1550157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.48 % (1550157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.48 % (1550157)CaDiCaL version: 2.1.3
% 3.58/1.48 % (1550157)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.48 % (1550157)Time elapsed: 0.004 s
% 3.58/1.48 % (1550157)Peak memory usage: 89 MB
% 3.58/1.48 % (1550157)Instructions burned: 5 (million)
% 3.58/1.48 % (1550151)Refutation found. Thanks to Tanya!
% 3.58/1.48 % SZS status Theorem for theBenchmark
% 3.58/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 4.98/1.68 % (1550151)------------------------------
% 4.98/1.68 % (1550151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.98/1.68 % (1550151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.98/1.68 % (1550151)CaDiCaL version: 2.1.3
% 4.98/1.68 % (1550151)Termination reason: Refutation
% 4.98/1.68 % (1550151)Time elapsed: 0.017 s
% 4.98/1.68 % (1550151)Peak memory usage: 90 MB
% 4.98/1.68 % (1550151)Instructions burned: 21 (million)
% 4.98/1.68 % (1550151)------------------------------
% 4.98/1.68 % (1550151)------------------------------
% 4.98/1.68 % (1550132)Success in time 0.622 s
% 4.98/1.68 % Vampire exiting
%------------------------------------------------------------------------------