%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n001.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 11:48:37 AM UTC 2026
% Result : Theorem 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 23
% Syntax : Number of formulae : 150 ( 24 unt; 9 def)
% Number of atoms : 454 ( 70 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 532 ( 228 ~; 225 |; 42 &)
% ( 19 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 10 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 188 ( 0 sgn 180 !; 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(f77,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(f78,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,[],[f77]) ).
fof(f96,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(f97,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,[],[f96]) ).
fof(f98,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(f99,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(f100,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(flattening,[],[f99]) ).
fof(f101,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(f102,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,[],[f101]) ).
fof(f104,plain,
! [X0] :
( l1_altcat_1(X0)
| ~ l2_altcat_1(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0,X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f106,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(f129,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f133,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f135,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)],[f78]) ).
fof(f136,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,[],[f100]) ).
fof(f137,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,[],[f102]) ).
fof(f150,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(f151,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,[],[f150]) ).
fof(f152,plain,
l2_altcat_1(sK0),
inference(cnf_transformation,[],[f135]) ).
fof(f154,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,[],[f135]) ).
fof(f155,plain,
r2_hidden(sK3,k1_binop_1(u1_altcat_1(sK0),sK1,sK2)),
inference(cnf_transformation,[],[f135]) ).
fof(f186,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f18]) ).
fof(f187,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,[],[f97]) ).
fof(f188,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,[],[f98]) ).
fof(f189,plain,
! [X0,X1] :
( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f192,plain,
! [X2,X0,X1] :
( k1_funct_1(X0,X1) = X2
| k1_xboole_0 != X2
| r2_hidden(X1,k1_relat_1(X0))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f195,plain,
! [X0,X1] : k4_tarski(X0,X1) = k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f197,plain,
! [X0] :
( ~ l2_altcat_1(X0)
| l1_altcat_1(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f198,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_funct_1(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f199,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_relat_1(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f200,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,[],[f106]) ).
fof(f245,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f58]) ).
fof(f271,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X1,X3)
| ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f272,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,X2)
| ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f274,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f277,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f279,plain,
! [X2,X0,X1] :
( k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(definition_unfolding,[],[f187,f195]) ).
fof(f283,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k2_zfmisc_1(X2,X3)) ),
inference(definition_unfolding,[],[f272,f195]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X1,X3)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k2_zfmisc_1(X2,X3)) ),
inference(definition_unfolding,[],[f271,f195]) ).
fof(f285,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,[],[f154]) ).
fof(f286,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,[],[f285]) ).
fof(f289,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,[],[f192]) ).
fof(f292,definition,
( spl16_1
<=> m1_subset_1(sK1,u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f293,plain,
( m1_subset_1(sK1,u1_struct_0(sK0))
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f296,definition,
( spl16_2
<=> m1_subset_1(sK2,u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f297,plain,
( m1_subset_1(sK2,u1_struct_0(sK0))
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f300,definition,
( spl16_3
<=> m1_subset_1(sK3,k1_altcat_1(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f302,plain,
( ~ m1_subset_1(sK3,k1_altcat_1(sK0,sK1,sK2))
| spl16_3 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f304,definition,
( spl16_4
<=> r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f307,plain,
( ~ spl16_1
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f286,f304,f300,f296,f292]) ).
fof(f335,plain,
l1_altcat_1(sK0),
inference(resolution,[],[f197,f152]) ).
fof(f362,plain,
~ v1_xboole_0(k1_binop_1(u1_altcat_1(sK0),sK1,sK2)),
inference(resolution,[],[f277,f155]) ).
fof(f364,plain,
m1_subset_1(sK3,k1_binop_1(u1_altcat_1(sK0),sK1,sK2)),
inference(resolution,[],[f274,f155]) ).
fof(f500,plain,
! [X0] :
( v1_relat_1(u1_altcat_1(X0))
| ~ l1_altcat_1(X0) ),
inference(resolution,[],[f200,f199]) ).
fof(f501,plain,
! [X0] :
( v1_funct_1(u1_altcat_1(X0))
| ~ l1_altcat_1(X0) ),
inference(resolution,[],[f200,f198]) ).
fof(f502,plain,
! [X0,X1] :
( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0)
| ~ v1_funct_1(X1) ),
inference(forward_subsumption_resolution,[],[f189,f199]) ).
fof(f503,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 ),
inference(forward_subsumption_resolution,[],[f502,f198]) ).
fof(f506,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(resolution,[],[f503,f200]) ).
fof(f508,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),k2_zfmisc_1(X2,X3))
| r2_hidden(X0,X2) ),
inference(forward_demodulation,[],[f283,f186]) ).
fof(f509,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),k2_zfmisc_1(X2,X3))
| r2_hidden(X1,X3) ),
inference(forward_demodulation,[],[f284,f186]) ).
fof(f528,plain,
! [X2,X0,X1] :
( ~ v1_relat_1(X0)
| k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))
| ~ v1_funct_1(X0) ),
inference(forward_demodulation,[],[f279,f186]) ).
fof(f576,plain,
k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)) = k1_relat_1(u1_altcat_1(sK0)),
inference(resolution,[],[f506,f335]) ).
fof(f581,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(superposition,[],[f509,f576]) ).
fof(f582,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(superposition,[],[f508,f576]) ).
fof(f632,definition,
( spl16_19
<=> v1_relat_1(u1_altcat_1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition]) ).
fof(f633,plain,
( v1_relat_1(u1_altcat_1(sK0))
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f634,plain,
( ~ v1_relat_1(u1_altcat_1(sK0))
| spl16_19 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f644,plain,
( ~ l1_altcat_1(sK0)
| spl16_19 ),
inference(resolution,[],[f634,f500]) ).
fof(f645,plain,
( $false
| spl16_19 ),
inference(forward_subsumption_resolution,[],[f644,f335]) ).
fof(f646,plain,
spl16_19,
inference(avatar_contradiction_clause,[],[f645]) ).
fof(f651,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)))
| ~ v1_funct_1(u1_altcat_1(sK0)) )
| ~ spl16_19 ),
inference(resolution,[],[f633,f528]) ).
fof(f653,definition,
( spl16_21
<=> v1_funct_1(u1_altcat_1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_21])],[avatar_definition]) ).
fof(f654,plain,
( v1_funct_1(u1_altcat_1(sK0))
| ~ spl16_21 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f655,plain,
( ~ v1_funct_1(u1_altcat_1(sK0))
| spl16_21 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f657,definition,
( spl16_22
<=> ! [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))) ),
introduced(definition,[new_symbols(definition,[spl16_22])],[avatar_definition]) ).
fof(f658,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)))
| ~ spl16_22 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f659,plain,
( ~ spl16_21
| spl16_22
| ~ spl16_19 ),
inference(avatar_split_clause,[],[f651,f632,f657,f653]) ).
fof(f664,plain,
( ~ l1_altcat_1(sK0)
| spl16_21 ),
inference(resolution,[],[f655,f501]) ).
fof(f665,plain,
( $false
| spl16_21 ),
inference(forward_subsumption_resolution,[],[f664,f335]) ).
fof(f666,plain,
spl16_21,
inference(avatar_contradiction_clause,[],[f665]) ).
fof(f683,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,[],[f581,f289]) ).
fof(f686,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)) )
| ~ spl16_19 ),
inference(forward_subsumption_resolution,[],[f683,f633]) ).
fof(f699,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))) )
| ~ spl16_19
| ~ spl16_21 ),
inference(forward_subsumption_resolution,[],[f686,f654]) ).
fof(f728,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,[],[f582,f289]) ).
fof(f731,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)) )
| ~ spl16_19 ),
inference(forward_subsumption_resolution,[],[f728,f633]) ).
fof(f732,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))) )
| ~ spl16_19
| ~ spl16_21 ),
inference(forward_subsumption_resolution,[],[f731,f654]) ).
fof(f1232,definition,
( spl16_66
<=> r2_hidden(sK1,u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_66])],[avatar_definition]) ).
fof(f1233,plain,
( r2_hidden(sK1,u1_struct_0(sK0))
| ~ spl16_66 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f1234,plain,
( ~ r2_hidden(sK1,u1_struct_0(sK0))
| spl16_66 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f1248,plain,
( ! [X0] : k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(sK1),k2_tarski(sK1,X0)))
| ~ spl16_19
| ~ spl16_21
| spl16_66 ),
inference(resolution,[],[f1234,f732]) ).
fof(f1252,plain,
( ! [X0] : k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),sK1,X0)
| ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_66 ),
inference(forward_demodulation,[],[f1248,f658]) ).
fof(f1268,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_66 ),
inference(superposition,[],[f362,f1252]) ).
fof(f1288,plain,
( $false
| ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_66 ),
inference(forward_subsumption_resolution,[],[f1268,f245]) ).
fof(f1289,plain,
( ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_66 ),
inference(avatar_contradiction_clause,[],[f1288]) ).
fof(f1294,plain,
( m1_subset_1(sK1,u1_struct_0(sK0))
| ~ spl16_66 ),
inference(resolution,[],[f1233,f274]) ).
fof(f1299,plain,
( spl16_1
| ~ spl16_66 ),
inference(avatar_split_clause,[],[f1294,f1232,f292]) ).
fof(f1349,definition,
( spl16_70
<=> r2_hidden(sK2,u1_struct_0(sK0)) ),
introduced(definition,[new_symbols(definition,[spl16_70])],[avatar_definition]) ).
fof(f1350,plain,
( r2_hidden(sK2,u1_struct_0(sK0))
| ~ spl16_70 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f1351,plain,
( ~ r2_hidden(sK2,u1_struct_0(sK0))
| spl16_70 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f1366,plain,
( ! [X0] : k1_xboole_0 = k1_funct_1(u1_altcat_1(sK0),k2_tarski(k1_tarski(X0),k2_tarski(X0,sK2)))
| ~ spl16_19
| ~ spl16_21
| spl16_70 ),
inference(resolution,[],[f1351,f699]) ).
fof(f1368,plain,
( ! [X0] : k1_xboole_0 = k1_binop_1(u1_altcat_1(sK0),X0,sK2)
| ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_70 ),
inference(forward_demodulation,[],[f1366,f658]) ).
fof(f1389,plain,
( ~ v1_xboole_0(k1_xboole_0)
| ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_70 ),
inference(superposition,[],[f362,f1368]) ).
fof(f1409,plain,
( $false
| ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_70 ),
inference(forward_subsumption_resolution,[],[f1389,f245]) ).
fof(f1410,plain,
( ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_70 ),
inference(avatar_contradiction_clause,[],[f1409]) ).
fof(f1415,plain,
( m1_subset_1(sK2,u1_struct_0(sK0))
| ~ spl16_70 ),
inference(resolution,[],[f1350,f274]) ).
fof(f1420,plain,
( spl16_2
| ~ spl16_70 ),
inference(avatar_split_clause,[],[f1415,f1349,f296]) ).
fof(f1423,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) )
| ~ spl16_2 ),
inference(resolution,[],[f297,f188]) ).
fof(f1441,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) )
| ~ spl16_2 ),
inference(forward_subsumption_resolution,[],[f1423,f335]) ).
fof(f1463,plain,
( k1_binop_1(u1_altcat_1(sK0),sK1,sK2) = k1_altcat_1(sK0,sK1,sK2)
| ~ spl16_1
| ~ spl16_2 ),
inference(resolution,[],[f1441,f293]) ).
fof(f1466,plain,
( r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ spl16_1
| ~ spl16_2 ),
inference(superposition,[],[f155,f1463]) ).
fof(f1469,plain,
( m1_subset_1(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ spl16_1
| ~ spl16_2 ),
inference(superposition,[],[f364,f1463]) ).
fof(f1477,plain,
( $false
| ~ spl16_1
| ~ spl16_2
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f1469,f302]) ).
fof(f1478,plain,
( ~ spl16_1
| ~ spl16_2
| spl16_3 ),
inference(avatar_contradiction_clause,[],[f1477]) ).
fof(f1479,plain,
( spl16_4
| ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f1466,f296,f292,f304]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4 ),
inference(sat_conversion,[],[f307]) ).
cnf(s12,plain,
spl16_19,
inference(sat_conversion,[],[f646]) ).
cnf(s13,plain,
( ~ spl16_19
| ~ spl16_21
| spl16_22 ),
inference(sat_conversion,[],[f659]) ).
cnf(s14,plain,
spl16_21,
inference(sat_conversion,[],[f666]) ).
cnf(s56,plain,
( ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_66 ),
inference(sat_conversion,[],[f1289]) ).
cnf(s58,plain,
( spl16_1
| ~ spl16_66 ),
inference(sat_conversion,[],[f1299]) ).
cnf(s67,plain,
( ~ spl16_19
| ~ spl16_21
| ~ spl16_22
| spl16_70 ),
inference(sat_conversion,[],[f1410]) ).
cnf(s69,plain,
( spl16_2
| ~ spl16_70 ),
inference(sat_conversion,[],[f1420]) ).
cnf(s70,plain,
( ~ spl16_1
| ~ spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f1478]) ).
cnf(s71,plain,
( ~ spl16_1
| ~ spl16_2
| spl16_4 ),
inference(sat_conversion,[],[f1479]) ).
cnf(s72,plain,
( ~ spl16_19
| spl16_22 ),
inference(rat,[],[s13,s14]) ).
cnf(s73,plain,
spl16_22,
inference(rat,[],[s72,s12]) ).
cnf(s74,plain,
spl16_70,
inference(rat,[],[s67,s12,s14,s73]) ).
cnf(s75,plain,
spl16_66,
inference(rat,[],[s56,s12,s14,s73]) ).
cnf(s76,plain,
spl16_2,
inference(rat,[],[s69,s74]) ).
cnf(s77,plain,
spl16_1,
inference(rat,[],[s58,s75]) ).
cnf(s78,plain,
spl16_4,
inference(rat,[],[s71,s76,s77]) ).
cnf(s79,plain,
spl16_3,
inference(rat,[],[s70,s76,s77]) ).
cnf(s81,plain,
$false,
inference(rat,[],[s1,s78,s79,s76,s77]) ).
fof(f1480,plain,
$false,
inference(avatar_sat_refutation,[],[s81]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:06:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.49 % (3667345)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (3667355)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1034832940:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % (3667351)% WARNING: option uhcvi not known.
% 0.16/0.49 % (3667352)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2791250403:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (3667350)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1950102911_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (3667351)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=61949347:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (3667353)dis+10_1_sil=32000:sp=arity:random_seed=3174569313:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (3667354)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1080754768:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (3667356)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=450780485:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % (3667353) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3667345-3667353"...
% 0.16/0.49 % (3667353)...printing done.
% 0.16/0.49 % (3667353)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Theorem for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (3667353)------------------------------
% 0.16/0.49 % (3667353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (3667353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (3667353)CaDiCaL version: 2.1.3
% 0.16/0.49 % (3667353)Termination reason: Refutation
% 0.16/0.49 % (3667353)Time elapsed: 0.032 s
% 0.16/0.49 % (3667353)Peak memory usage: 13 MB
% 0.16/0.49 % (3667353)Instructions burned: 47 (million)
% 0.16/0.49 % (3667345)Success in time 0.07 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------