%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT359+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:59:38 PM UTC 2026
% Result : Theorem 8.17s 1.63s
% Output : CNFRefutation 8.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 20
% Syntax : Number of formulae : 136 ( 37 unt; 6 def)
% Number of atoms : 459 ( 110 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 410 ( 172 ~; 168 |; 42 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 234 ( 0 sgn 226 !; 8 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l2_altcat_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1,X2,X3] :
~ ( ! [X4] :
( m1_subset_1(X4,u1_struct_0(X0))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(X0))
=> ~ ( m1_subset_1(X3,k1_altcat_1(X0,X4,X5))
& r2_hidden(X3,k1_altcat_1(X0,X4,X5))
& X5 = X2
& X4 = X1 ) ) )
& r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_waybel34) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l2_altcat_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1,X2,X3] :
~ ( ! [X4] :
( m1_subset_1(X4,u1_struct_0(X0))
=> ! [X5] :
( m1_subset_1(X5,u1_struct_0(X0))
=> ~ ( m1_subset_1(X3,k1_altcat_1(X0,X4,X5))
& r2_hidden(X3,k1_altcat_1(X0,X4,X5))
& X5 = X2
& X4 = X1 ) ) )
& r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2)) ) ),
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_funct_1(X0)
& v1_relat_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_funct_1(X1)
& v1_relat_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_funct_1(X0)
& v1_relat_1(X0) )
=> ! [X1,X2] :
( ( ~ r2_hidden(X1,k1_relat_1(X0))
=> ( X2 = k1_funct_1(X0,X1)
<=> X2 = k1_xboole_0 ) )
& ( r2_hidden(X1,k1_relat_1(X0))
=> ( X2 = k1_funct_1(X0,X1)
<=> r2_hidden(k4_tarski(X1,X2),X0) ) ) ) ),
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_funct_1(X1)
& v1_relat_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,
( v5_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v1_xboole_0(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(X1,X3)
& r2_hidden(X0,X2) ) ),
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] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f77,plain,
? [X0] :
( l2_altcat_1(X0)
& ~ v3_struct_0(X0)
& ? [X1,X2,X3] :
( ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(X0))
| ! [X5] :
( ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ m1_subset_1(X3,k1_altcat_1(X0,X4,X5))
| ~ r2_hidden(X3,k1_altcat_1(X0,X4,X5))
| X2 != X5
| X1 != X4 ) )
& r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f78,plain,
? [X0] :
( l2_altcat_1(X0)
& ~ v3_struct_0(X0)
& ? [X1,X2,X3] :
( ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(X0))
| ! [X5] :
( ~ m1_subset_1(X5,u1_struct_0(X0))
| ~ m1_subset_1(X3,k1_altcat_1(X0,X4,X5))
| ~ r2_hidden(X3,k1_altcat_1(X0,X4,X5))
| X2 != X5
| X1 != X4 ) )
& r2_hidden(X3,k1_binop_1(u1_altcat_1(X0),X1,X2)) ) ),
inference(flattening,[],[f77]) ).
fof(f96,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1,X2] : k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k4_tarski(X1,X2)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f97,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1,X2] : k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k4_tarski(X1,X2)) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [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) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f99,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f100,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( r2_hidden(X1,k1_relat_1(X0))
| ( X2 = k1_funct_1(X0,X1)
<=> X2 = k1_xboole_0 ) )
& ( ~ r2_hidden(X1,k1_relat_1(X0))
| ( X2 = k1_funct_1(X0,X1)
<=> r2_hidden(k4_tarski(X1,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f102,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( r2_hidden(X1,k1_relat_1(X0))
| ( X2 = k1_funct_1(X0,X1)
<=> X2 = k1_xboole_0 ) )
& ( ~ r2_hidden(X1,k1_relat_1(X0))
| ( X2 = k1_funct_1(X0,X1)
<=> r2_hidden(k4_tarski(X1,X2),X0) ) ) ) ),
inference(flattening,[],[f101]) ).
fof(f104,plain,
! [X0] :
( ~ l2_altcat_1(X0)
| l1_altcat_1(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ( v1_funct_1(X1)
& v1_relat_1(X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f106,plain,
! [X0] :
( ~ l1_altcat_1(X0)
| m1_pboole(u1_altcat_1(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f38]) ).
fof(f129,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f133,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f135,plain,
( l2_altcat_1(sK0)
& ~ v3_struct_0(sK0)
& ! [X4] :
( ~ m1_subset_1(X4,u1_struct_0(sK0))
| ! [X5] :
( ~ m1_subset_1(X5,u1_struct_0(sK0))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,X4,X5))
| ~ r2_hidden(sK3,k1_altcat_1(sK0,X4,X5))
| sK2 != X5
| sK1 != X4 ) )
& r2_hidden(sK3,k1_binop_1(u1_altcat_1(sK0),sK1,sK2)) ),
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] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( ( ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 )
& ( k1_relat_1(X1) != X0
| m1_pboole(X1,X0) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f137,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1,X2] :
( ( r2_hidden(X1,k1_relat_1(X0))
| ( ( k1_funct_1(X0,X1) != X2
| X2 = k1_xboole_0 )
& ( k1_xboole_0 != X2
| X2 = k1_funct_1(X0,X1) ) ) )
& ( ~ r2_hidden(X1,k1_relat_1(X0))
| ( ( k1_funct_1(X0,X1) != X2
| r2_hidden(k4_tarski(X1,X2),X0) )
& ( ~ r2_hidden(k4_tarski(X1,X2),X0)
| X2 = k1_funct_1(X0,X1) ) ) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( ( ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3))
| ( r2_hidden(X1,X3)
& r2_hidden(X0,X2) ) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,X2)
| 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(X1,X3)
& r2_hidden(X0,X2) ) )
& ( ~ r2_hidden(X1,X3)
| ~ r2_hidden(X0,X2)
| 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] :
( ~ m1_subset_1(X4,u1_struct_0(sK0))
| ~ m1_subset_1(X5,u1_struct_0(sK0))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,X4,X5))
| ~ r2_hidden(sK3,k1_altcat_1(sK0,X4,X5))
| sK2 != X5
| sK1 != X4 ),
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] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k4_tarski(X1,X2)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ l1_altcat_1(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| k1_binop_1(u1_altcat_1(X0),X1,X2) = k1_altcat_1(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f189,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 ),
inference(cnf_transformation,[],[f136]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| r2_hidden(X1,k1_relat_1(X0))
| k1_funct_1(X0,X1) != X2
| k1_xboole_0 = X2 ),
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] :
( ~ l1_altcat_1(X0)
| m1_pboole(u1_altcat_1(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(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(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3))
| r2_hidden(X1,X3) ),
inference(cnf_transformation,[],[f151]) ).
fof(f272,plain,
! [X2,X3,X0,X1] :
( ~ r2_hidden(k4_tarski(X0,X1),k2_zfmisc_1(X2,X3))
| r2_hidden(X0,X2) ),
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] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f279,plain,
! [X2,X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| k1_binop_1(X0,X1,X2) = k1_funct_1(X0,k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))) ),
inference(definition_unfolding,[],[f187,f195]) ).
fof(f283,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,[],[f272,f195]) ).
fof(f284,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,[],[f271,f195]) ).
fof(f285,plain,
! [X5] :
( ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(X5,u1_struct_0(sK0))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,sK1,X5))
| ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,X5))
| sK2 != X5 ),
inference(equality_resolution,[],[f154]) ).
fof(f286,plain,
( ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2)) ),
inference(equality_resolution,[],[f285]) ).
fof(f290,plain,
! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| r2_hidden(X1,k1_relat_1(X0))
| k1_funct_1(X0,X1) = k1_xboole_0 ),
inference(equality_resolution,[],[f191]) ).
tcf(c_49,negated_conjecture,
r2_hidden(sK3,k1_binop_1(u1_altcat_1(sK0),sK1,sK2)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_50,negated_conjecture,
( ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ m1_subset_1(sK3,k1_altcat_1(sK0,sK1,sK2))
| ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2)) ),
inference(cnf_transformation,[],[f286]) ).
tcf(c_52,negated_conjecture,
l2_altcat_1(sK0),
inference(cnf_transformation,[],[f152]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f186]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k1_funct_1(X0,k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))) = k1_binop_1(X0,X1,X2) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k1_binop_1(u1_altcat_1(X1),X0,X2) = k1_altcat_1(X1,X0,X2) )
| ~ l1_altcat_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,k1_relat_1(X0))
| ( k1_funct_1(X0,X1) = k1_xboole_0 )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_91,plain,
! [X0: $i] :
( l1_altcat_1(X0)
| ~ l2_altcat_1(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_94,plain,
! [X0: $i] :
( m1_pboole(u1_altcat_1(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)))
| ~ l1_altcat_1(X0) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_134,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f245]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X0,X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k2_zfmisc_1(X2,X3)) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X1,X3)
| ~ r2_hidden(k2_tarski(k2_tarski(X0,X1),k1_tarski(X0)),k2_zfmisc_1(X2,X3)) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ~ m1_pboole(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_93,c_92,c_85]) ).
tcf(c_457,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK0))
| ~ m1_subset_1(sK1,u1_struct_0(sK0))
| ~ r2_hidden(sK3,k1_altcat_1(sK0,sK1,sK2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_168]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X1,X3)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),k2_zfmisc_1(X2,X3)) ),
inference(demodulation,[status(thm)],[c_167,c_81]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( r2_hidden(X0,X2)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),k2_zfmisc_1(X2,X3)) ),
inference(demodulation,[status(thm)],[c_166,c_81]) ).
tcf(c_1170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k1_funct_1(X0,k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))) = k1_binop_1(X0,X1,X2) )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(demodulation,[status(thm)],[c_82,c_81]) ).
tcf(c_1248,plain,
! [X0: $i] :
( l1_altcat_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_91]) ).
tcf(c_1249,plain,
l1_altcat_1(sK0),
inference(unflattening,[status(thm)],[c_1248]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k1_binop_1(u1_altcat_1(X0),X1,X2) = k1_altcat_1(X0,X1,X2) )
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_1249]) ).
tcf(c_1353,plain,
! [X0: $i,X1: $i] :
( ( k1_binop_1(u1_altcat_1(sK0),X0,X1) = k1_altcat_1(sK0,X0,X1) )
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1352]) ).
tcf(c_1381,plain,
! [X0: $i] :
( m1_pboole(u1_altcat_1(X0),k2_zfmisc_1(u1_struct_0(X0),u1_struct_0(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_1249]) ).
tcf(c_1382,plain,
m1_pboole(u1_altcat_1(sK0),k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0))),
inference(unflattening,[status(thm)],[c_1381]) ).
tcf(c_1442,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ( u1_altcat_1(sK0) != X0 )
| ( k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_250,c_1382]) ).
tcf(c_1443,plain,
k1_relat_1(u1_altcat_1(sK0)) = k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)),
inference(unflattening,[status(thm)],[c_1442]) ).
tcf(c_1447,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| ( u1_altcat_1(sK0) != X0 )
| ( k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_93,c_1382]) ).
tcf(c_1448,plain,
v1_funct_1(u1_altcat_1(sK0)),
inference(unflattening,[status(thm)],[c_1447]) ).
tcf(c_1452,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(X0)
| ( u1_altcat_1(sK0) != X0 )
| ( k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK0)) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_92,c_1382]) ).
tcf(c_1453,plain,
v1_relat_1(u1_altcat_1(sK0)),
inference(unflattening,[status(thm)],[c_1452]) ).
tcf(c_3355,definition,
iPr_def_10 = u1_altcat_1(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3356,definition,
iPr_def_11 = k1_relat_1(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3357,definition,
iPr_def_12 = u1_struct_0(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3358,definition,
iPr_def_13 = k2_zfmisc_1(iPr_def_12,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_3359,definition,
iPr_def_14 = k1_altcat_1(sK0,sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_3360,definition,
iPr_def_15 = k1_binop_1(iPr_def_10,sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_3361,plain,
v1_relat_1(iPr_def_10),
inference(demodulation,[status(thm)],[c_1453,c_3355]) ).
tcf(c_3362,plain,
v1_funct_1(iPr_def_10),
inference(demodulation,[status(thm)],[c_1448]) ).
tcf(c_3363,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_1443,c_3357,c_3358,c_3356]) ).
tcf(c_3364,plain,
! [X0: $i,X1: $i] :
( ( k1_binop_1(iPr_def_10,X0,X1) = k1_altcat_1(sK0,X0,X1) )
| ~ m1_subset_1(X1,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_1353]) ).
tcf(c_3366,plain,
( ~ m1_subset_1(sK2,iPr_def_12)
| ~ m1_subset_1(sK1,iPr_def_12)
| ~ r2_hidden(sK3,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_457,c_3359]) ).
tcf(c_3367,negated_conjecture,
r2_hidden(sK3,iPr_def_15),
inference(demodulation,[status(thm)],[c_49,c_3360]) ).
tcf(c_4005,plain,
k2_zfmisc_1(iPr_def_12,iPr_def_12) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3358,c_3363]) ).
tcf(c_4006,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_12)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4005,c_1139]) ).
tcf(c_4007,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,iPr_def_12)
| ~ r2_hidden(k2_tarski(k1_tarski(X0),k2_tarski(X0,X1)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4005,c_1132]) ).
tcf(c_4053,plain,
~ v1_xboole_0(iPr_def_15),
inference(superposition,[status(thm)],[c_3367,c_171]) ).
tcf(c_4317,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_11)
| ( k1_funct_1(iPr_def_10,X0) = k1_xboole_0 )
| ~ v1_relat_1(iPr_def_10)
| ~ v1_funct_1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3356,c_89]) ).
tcf(c_4321,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_11)
| ( k1_funct_1(iPr_def_10,X0) = k1_xboole_0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4317,c_3361,c_3362]) ).
tcf(c_4356,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(iPr_def_10,k2_tarski(k1_tarski(X0),k2_tarski(X0,X1))) = k1_binop_1(iPr_def_10,X0,X1) )
| ~ v1_funct_1(iPr_def_10) ),
inference(superposition,[status(thm)],[c_3361,c_1170]) ).
tcf(c_4357,plain,
! [X0: $i,X1: $i] : k1_funct_1(iPr_def_10,k2_tarski(k1_tarski(X0),k2_tarski(X0,X1))) = k1_binop_1(iPr_def_10,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[c_4356,c_3362]) ).
tcf(c_4433,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,iPr_def_12)
| ( k1_funct_1(iPr_def_10,k2_tarski(k1_tarski(X0),k2_tarski(X0,X1))) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_4321,c_4007]) ).
tcf(c_4434,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_12)
| ( k1_funct_1(iPr_def_10,k2_tarski(k1_tarski(X0),k2_tarski(X0,X1))) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_4321,c_4006]) ).
tcf(c_4445,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,iPr_def_12)
| ( k1_binop_1(iPr_def_10,X0,X1) = k1_xboole_0 ) ),
inference(light_normalisation,[status(thm)],[c_4434,c_4357]) ).
tcf(c_4448,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X1,iPr_def_12)
| ( k1_binop_1(iPr_def_10,X0,X1) = k1_xboole_0 ) ),
inference(light_normalisation,[status(thm)],[c_4433,c_4357]) ).
tcf(c_4791,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,iPr_def_12)
| ( k1_binop_1(iPr_def_10,X0,X1) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_4445,c_168]) ).
tcf(c_4815,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X1,iPr_def_12)
| ( k1_binop_1(iPr_def_10,X0,X1) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_4448,c_168]) ).
tcf(c_4972,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k1_binop_1(iPr_def_10,X1,X2) = k1_xboole_0 )
| ( k1_binop_1(iPr_def_10,X1,X0) = k1_altcat_1(sK0,X1,X0) )
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_4791,c_3364]) ).
tcf(c_5430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( k1_binop_1(iPr_def_10,X2,X3) = k1_xboole_0 )
| ( k1_binop_1(iPr_def_10,X2,X1) = k1_altcat_1(sK0,X2,X1) )
| ( k1_binop_1(iPr_def_10,X0,X1) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_4815,c_4972]) ).
tcf(c_6770,plain,
! [X0: $i,X1: $i] :
( ( k1_xboole_0 = iPr_def_15 )
| ( k1_binop_1(iPr_def_10,sK1,X1) = k1_altcat_1(sK0,sK1,X1) )
| ( k1_binop_1(iPr_def_10,X0,X1) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_5430,c_3360]) ).
tcf(c_8960,plain,
( ( k1_xboole_0 = iPr_def_15 )
| ( k1_binop_1(iPr_def_10,sK1,sK2) = k1_altcat_1(sK0,sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_6770,c_3360]) ).
tcf(c_8966,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( k1_xboole_0 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8960,c_3359,c_3360]) ).
tcf(c_9229,plain,
( v1_xboole_0(iPr_def_15)
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_8966,c_134]) ).
tcf(c_9230,plain,
iPr_def_14 = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_9229,c_4053]) ).
tcf(c_9262,plain,
k1_binop_1(iPr_def_10,sK1,sK2) = iPr_def_14,
inference(demodulation,[status(thm)],[c_3360,c_9230]) ).
tcf(c_9263,plain,
~ v1_xboole_0(iPr_def_14),
inference(demodulation,[status(thm)],[c_4053,c_9230]) ).
tcf(c_9265,plain,
r2_hidden(sK3,iPr_def_14),
inference(demodulation,[status(thm)],[c_3367,c_9230]) ).
tcf(c_9266,plain,
( ~ m1_subset_1(sK2,iPr_def_12)
| ~ m1_subset_1(sK1,iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3366,c_9265]) ).
tcf(c_9359,plain,
! [X0: $i] :
( ( k1_binop_1(iPr_def_10,sK1,X0) = k1_xboole_0 )
| ~ m1_subset_1(sK2,iPr_def_12) ),
inference(superposition,[status(thm)],[c_4791,c_9266]) ).
tcf(c_9560,plain,
! [X0: $i,X1: $i] :
( ( k1_binop_1(iPr_def_10,sK1,X1) = k1_xboole_0 )
| ( k1_binop_1(iPr_def_10,X0,sK2) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_4815,c_9359]) ).
tcf(c_11105,plain,
( ( k1_binop_1(iPr_def_10,sK1,sK2) = k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(equality_factoring,[status(thm)],[c_9560]) ).
tcf(c_11111,plain,
k1_binop_1(iPr_def_10,sK1,sK2) = k1_xboole_0,
inference(equality_resolution_simp,[status(thm)],[c_11105]) ).
tcf(c_11112,plain,
k1_xboole_0 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_11111,c_9262]) ).
tcf(c_11292,plain,
v1_xboole_0(iPr_def_14),
inference(demodulation,[status(thm)],[c_134,c_11112]) ).
tcf(c_11293,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11292,c_9263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT359+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 21:25:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 8.17/1.63 % SZS status Started for theBenchmark.p
% 8.17/1.63 % SZS status Theorem for theBenchmark.p
% 8.17/1.63
% 8.17/1.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.17/1.63
% 8.17/1.63 % ------ iProver source info
% 8.17/1.63
% 8.17/1.63 % git: date: 2026-07-19 20:42:38 +0200
% 8.17/1.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.17/1.63 % git: non_committed_changes: false
% 8.17/1.63
% 8.17/1.63 % ------ Parsing...
% 8.17/1.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.17/1.63
% 8.17/1.63 % ------ Preprocessing... sup_sim: 6 sf_s rm: 76 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe_e %
% 8.17/1.63
% 8.17/1.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.17/1.63
% 8.17/1.63 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.17/1.63 % ------ Proving...
% 8.17/1.63 % ------ Problem Properties
% 8.17/1.63
% 8.17/1.63 %
% 8.17/1.63 % clauses 58
% 8.17/1.63 % conjectures 1
% 8.17/1.63 % EPR 26
% 8.17/1.63 % Horn 54
% 8.17/1.63 % unary 37
% 8.17/1.63 % binary 8
% 8.17/1.63 % lits 97
% 8.17/1.63 % lits eq 19
% 8.17/1.63 % fd_pure 0
% 8.17/1.63 % fd_pseudo 0
% 8.17/1.63 % fd_cond 1
% 8.17/1.63 % fd_pseudo_cond 2
% 8.17/1.63 % AC symbols 0
% 8.17/1.63
% 8.17/1.63 % ------ Schedule dynamic 5 is on
% 8.17/1.63
% 8.17/1.63 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.17/1.63
% 8.17/1.63
% 8.17/1.63 % ------
% 8.17/1.63 % Current options:
% 8.17/1.63 % ------
% 8.17/1.63
% 8.17/1.63
% 8.17/1.63 %
% 8.17/1.63
% 8.17/1.63 % ------ Proving...
% 8.17/1.63 %
% 8.17/1.63
% 8.17/1.63 % SZS status Theorem for theBenchmark.p
% 8.17/1.63
% 8.17/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.17/1.64
% 8.17/1.64
%------------------------------------------------------------------------------