%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT328+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 01:59:20 PM UTC 2026
% Result : Theorem 3.77s 1.20s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 23
% Syntax : Number of formulae : 266 ( 31 unt; 3 def)
% Number of atoms : 1515 ( 85 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 1735 ( 748 ~; 840 |; 102 &)
% ( 12 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 475 ( 0 sgn 466 !; 9 ?; 245 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r1_filter_2(u1_struct_0(X0),k22_filter_2(X0,X1,X1),k6_domain_1(u1_struct_0(X0),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_filter_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> r1_filter_2(u1_struct_0(X0),k22_filter_2(X0,X1,X1),k6_domain_1(u1_struct_0(X0),X1)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0] :
( l3_lattices(X0)
=> ( ( v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v9_lattices(X0)
& v8_lattices(X0)
& v7_lattices(X0)
& v6_lattices(X0)
& v5_lattices(X0)
& v4_lattices(X0)
& ~ v3_struct_0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).
fof(f8,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ( r1_filter_2(X0,X1,X2)
<=> ! [X3] :
( m1_subset_1(X3,X0)
=> ( r2_hidden(X3,X1)
<=> r2_hidden(X3,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).
fof(f9,axiom,
! [X0,X1] :
( X1 = k1_tarski(X0)
<=> ! [X2] :
( r2_hidden(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( m2_lattice4(k22_filter_2(X0,X1,X2),X0)
& ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).
fof(f14,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,X0)
& ~ v1_xboole_0(X0) )
=> m1_subset_1(k6_domain_1(X0,X1),k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
fof(f15,axiom,
! [X0] :
( l1_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f17,axiom,
! [X0] :
( l2_lattices(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f18,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l2_lattices(X0)
& l1_lattices(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f20,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_lattice4(X1,X0)
=> m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(f28,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f42,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,X0)
& ~ v1_xboole_0(X0) )
=> k6_domain_1(X0,X1) = k1_tarski(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
fof(f44,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v9_lattices(X0)
& v8_lattices(X0)
& v6_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( r3_lattices(X0,X1,X2)
<=> r1_lattices(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(f47,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v9_lattices(X0)
& v8_lattices(X0)
& v6_lattices(X0)
& ~ v3_struct_0(X0) )
=> r3_lattices(X0,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(f49,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f50,axiom,
! [X0] :
( ( l2_lattices(X0)
& v4_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( ( r1_lattices(X0,X2,X1)
& r1_lattices(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
fof(f51,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(f53,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(f54,axiom,
! [X0,X1,X2] :
~ ( v1_xboole_0(X2)
& m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f55,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X0))
=> ( r3_lattices(X0,X1,X2)
=> ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_2) ).
fof(f63,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ~ r1_filter_2(u1_struct_0(X0),k22_filter_2(X0,X1,X1),k6_domain_1(u1_struct_0(X0),X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f64,plain,
? [X0] :
( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0)
& ? [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
& ~ r1_filter_2(u1_struct_0(X0),k22_filter_2(X0,X1,X1),k6_domain_1(u1_struct_0(X0),X1)) ) ),
inference(flattening,[],[f63]) ).
fof(f66,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v9_lattices(X0)
& v8_lattices(X0)
& v7_lattices(X0)
& v6_lattices(X0)
& v5_lattices(X0)
& v4_lattices(X0)
& ~ v3_struct_0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f67,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( v9_lattices(X0)
& v8_lattices(X0)
& v7_lattices(X0)
& v6_lattices(X0)
& v5_lattices(X0)
& v4_lattices(X0)
& ~ v3_struct_0(X0) ) ),
inference(flattening,[],[f66]) ).
fof(f71,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( r1_filter_2(X0,X1,X2)
<=> ! [X3] :
( ~ m1_subset_1(X3,X0)
| ( r2_hidden(X3,X1)
<=> r2_hidden(X3,X2) ) ) ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( m2_lattice4(k22_filter_2(X0,X1,X2),X0)
& ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ( m2_lattice4(k22_filter_2(X0,X1,X2),X0)
& ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| m1_subset_1(k6_domain_1(X0,X1),k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f75,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| m1_subset_1(k6_domain_1(X0,X1),k1_zfmisc_1(X0)) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f77,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f78,plain,
! [X0] :
( ~ l3_lattices(X0)
| ( l2_lattices(X0)
& l1_lattices(X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f79,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_lattice4(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f80,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_lattice4(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(flattening,[],[f79]) ).
fof(f83,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f84,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f83]) ).
fof(f90,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f91,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(flattening,[],[f90]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| ( r3_lattices(X0,X1,X2)
<=> r1_lattices(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| ( r3_lattices(X0,X1,X2)
<=> r1_lattices(X0,X1,X2) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| r3_lattices(X0,X1,X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| r3_lattices(X0,X1,X1) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f103,plain,
! [X0] :
( ~ l2_lattices(X0)
| ~ v4_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r1_lattices(X0,X2,X1)
| ~ r1_lattices(X0,X1,X2)
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f104,plain,
! [X0] :
( ~ l2_lattices(X0)
| ~ v4_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r1_lattices(X0,X2,X1)
| ~ r1_lattices(X0,X1,X2)
| X1 = X2 ) ) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f106,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f105]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(ennf_transformation,[],[f53]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f111,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f112,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( r2_hidden(X3,k22_filter_2(X0,X1,X2))
<=> ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) ) ) ) ) ),
inference(flattening,[],[f111]) ).
fof(f116,plain,
( l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0)
& m1_subset_1(sK1,u1_struct_0(sK0))
& ~ r1_filter_2(u1_struct_0(sK0),k22_filter_2(sK0,sK1,sK1),k6_domain_1(u1_struct_0(sK0),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f64]) ).
fof(f117,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ( ( ~ r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1) ) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,X0)
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f118,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X3] :
( ~ m1_subset_1(X3,X0)
| ( ( ~ r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X2)
| r2_hidden(X3,X1) ) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,X0)
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X4] :
( ~ m1_subset_1(X4,X0)
| ( ( ~ r2_hidden(X4,X1)
| r2_hidden(X4,X2) )
& ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ) )
& ( ? [X3] :
( m1_subset_1(X3,X0)
& ( r2_hidden(X3,X1)
| r2_hidden(X3,X2) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ! [X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ( ( ~ r1_filter_2(X0,X1,X2)
| ! [X4] :
( ~ m1_subset_1(X4,X0)
| ( ( ~ r2_hidden(X4,X1)
| r2_hidden(X4,X2) )
& ( ~ r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ) )
& ( ( m1_subset_1(sK2(X0,X1,X2),X0)
& ( r2_hidden(sK2(X0,X1,X2),X1)
| r2_hidden(sK2(X0,X1,X2),X2) )
& ( ~ r2_hidden(sK2(X0,X1,X2),X1)
| ~ r2_hidden(sK2(X0,X1,X2),X2) ) )
| r1_filter_2(X0,X1,X2) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ( k1_tarski(X0) != X1
| ! [X2] :
( ( ~ r2_hidden(X2,X1)
| X2 = X0 )
& ( X0 != X2
| r2_hidden(X2,X1) ) ) )
& ( ? [X2] :
( ( r2_hidden(X2,X1)
| X2 = X0 )
& ( ~ r2_hidden(X2,X1)
| X0 != X2 ) )
| X1 = k1_tarski(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f122,plain,
! [X0,X1] :
( ( k1_tarski(X0) != X1
| ! [X3] :
( ( ~ r2_hidden(X3,X1)
| X0 = X3 )
& ( X0 != X3
| r2_hidden(X3,X1) ) ) )
& ( ? [X2] :
( ( r2_hidden(X2,X1)
| X2 = X0 )
& ( ~ r2_hidden(X2,X1)
| X0 != X2 ) )
| X1 = k1_tarski(X0) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( ( k1_tarski(X0) != X1
| ! [X3] :
( ( ~ r2_hidden(X3,X1)
| X0 = X3 )
& ( X0 != X3
| r2_hidden(X3,X1) ) ) )
& ( ( ( r2_hidden(sK3(X0,X1),X1)
| sK3(X0,X1) = X0 )
& ( ~ r2_hidden(sK3(X0,X1),X1)
| sK3(X0,X1) != X0 ) )
| X1 = k1_tarski(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f122]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| ( ( ~ r3_lattices(X0,X1,X2)
| r1_lattices(X0,X1,X2) )
& ( ~ r1_lattices(X0,X1,X2)
| r3_lattices(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f95]) ).
fof(f141,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( ( ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) )
& ( ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) ) ) ) ) ),
inference(nnf_transformation,[],[f112]) ).
fof(f142,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,u1_struct_0(X0))
| ! [X2] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( ( ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ( r3_lattices(X0,X3,X2)
& r3_lattices(X0,X1,X3) ) )
& ( ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ) ) ) ) ) ),
inference(flattening,[],[f141]) ).
fof(f143,plain,
l3_lattices(sK0),
inference(cnf_transformation,[],[f116]) ).
fof(f144,plain,
v10_lattices(sK0),
inference(cnf_transformation,[],[f116]) ).
fof(f145,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f116]) ).
fof(f146,plain,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f116]) ).
fof(f147,plain,
~ r1_filter_2(u1_struct_0(sK0),k22_filter_2(sK0,sK1,sK1),k6_domain_1(u1_struct_0(sK0),sK1)),
inference(cnf_transformation,[],[f116]) ).
fof(f149,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v9_lattices(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f150,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v8_lattices(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f152,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v6_lattices(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f154,plain,
! [X0] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| v4_lattices(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f161,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| m1_subset_1(sK2(X0,X1,X2),X0)
| r1_filter_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f162,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| r2_hidden(sK2(X0,X1,X2),X1)
| r2_hidden(sK2(X0,X1,X2),X2)
| r1_filter_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f163,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ r2_hidden(sK2(X0,X1,X2),X1)
| ~ r2_hidden(sK2(X0,X1,X2),X2)
| r1_filter_2(X0,X1,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f165,plain,
! [X3,X0,X1] :
( k1_tarski(X0) != X1
| X0 != X3
| r2_hidden(X3,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m2_lattice4(k22_filter_2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f170,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| m1_subset_1(k6_domain_1(X0,X1),k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f171,plain,
! [X0] :
( ~ l1_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f172,plain,
! [X0] :
( ~ l2_lattices(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f173,plain,
! [X0] :
( ~ l3_lattices(X0)
| l2_lattices(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f174,plain,
! [X0] :
( ~ l3_lattices(X0)
| l1_lattices(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f175,plain,
! [X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m2_lattice4(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f182,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f204,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0)
| k6_domain_1(X0,X1) = k1_tarski(X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| ~ r3_lattices(X0,X1,X2)
| r1_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f140]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0)
| r3_lattices(X0,X1,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f213,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ l2_lattices(X0)
| ~ v4_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ r1_lattices(X0,X2,X1)
| ~ r1_lattices(X0,X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f104]) ).
fof(f215,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| r3_lattices(X0,X3,X2) ),
inference(cnf_transformation,[],[f142]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ~ r2_hidden(X3,k22_filter_2(X0,X1,X2))
| r3_lattices(X0,X1,X3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f225,plain,
! [X3,X1] :
( k1_tarski(X3) != X1
| r2_hidden(X3,X1) ),
inference(equality_resolution,[],[f165]) ).
fof(f226,plain,
! [X3] : r2_hidden(X3,k1_tarski(X3)),
inference(equality_resolution,[],[f225]) ).
tcf(c_49,negated_conjecture,
~ r1_filter_2(u1_struct_0(sK0),k22_filter_2(sK0,sK1,sK1),k6_domain_1(u1_struct_0(sK0),sK1)),
inference(cnf_transformation,[],[f147]) ).
tcf(c_50,negated_conjecture,
m1_subset_1(sK1,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f146]) ).
tcf(c_51,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f145]) ).
tcf(c_52,negated_conjecture,
v10_lattices(sK0),
inference(cnf_transformation,[],[f144]) ).
tcf(c_53,negated_conjecture,
l3_lattices(sK0),
inference(cnf_transformation,[],[f143]) ).
tcf(c_55,plain,
! [X0: $i] :
( v4_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_57,plain,
! [X0: $i] :
( v6_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_59,plain,
! [X0: $i] :
( v8_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_60,plain,
! [X0: $i] :
( v9_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X0)
| r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ r2_hidden(sK2(X0,X1,X2),X2)
| ~ r2_hidden(sK2(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| r1_filter_2(X1,X0,X2)
| r2_hidden(sK2(X1,X0,X2),X2)
| r2_hidden(sK2(X1,X0,X2),X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| r1_filter_2(X1,X0,X2)
| m1_subset_1(sK2(X1,X0,X2),X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_70,plain,
! [X0: $i] : r2_hidden(X0,k1_tarski(X0)),
inference(cnf_transformation,[],[f226]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v1_xboole_0(k22_filter_2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m2_lattice4(k22_filter_2(X1,X0,X2),X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| m1_subset_1(k6_domain_1(X1,X0),k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_75,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_76,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l2_lattices(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_77,plain,
! [X0: $i] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_78,plain,
! [X0: $i] :
( l2_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_lattice4(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_86,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| ( k6_domain_1(X1,X0) = k1_tarski(X0) )
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_lattices(X0,X1,X2)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X0)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ v6_lattices(X1)
| ~ l3_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( X1 = X2 )
| ~ l2_lattices(X0)
| ~ v4_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r1_lattices(X0,X2,X1)
| ~ r1_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( m1_subset_1(X2,X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X1,X2) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X2,X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X3)
| ~ r2_hidden(X0,k22_filter_2(X1,X2,X3)) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X3)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X3)
| ~ r2_hidden(X0,k22_filter_2(X1,X2,X3)) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_137,plain,
( l2_lattices(sK0)
| ~ l3_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_139,plain,
( l1_struct_0(sK0)
| ~ l2_lattices(sK0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_151,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ r2_hidden(sK2(X0,X1,X2),X2)
| ~ r2_hidden(sK2(X0,X1,X2),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_122]) ).
tcf(c_1162,plain,
! [X0: $i,X1: $i] :
( l1_struct_0(X1)
| ~ l3_lattices(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_75]) ).
tcf(c_1163,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(unflattening,[status(thm)],[c_1162]) ).
tcf(c_1181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| ( X2 = X3 )
| ~ l2_lattices(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r1_lattices(X1,X3,X2)
| ~ r1_lattices(X1,X2,X3)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_118]) ).
tcf(c_1182,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( X1 = X2 )
| ~ l2_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r1_lattices(X0,X2,X1)
| ~ r1_lattices(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_1181]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( X1 = X2 )
| ~ r1_lattices(X0,X1,X2)
| ~ r1_lattices(X0,X2,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ v10_lattices(X0)
| ~ l3_lattices(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1182,c_78,c_1182]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( X1 = X2 )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r1_lattices(X0,X2,X1)
| ~ r1_lattices(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_1184]) ).
tcf(c_1227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( v3_struct_0(X4)
| v3_struct_0(X0)
| m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X4)))
| ~ l3_lattices(X4)
| ~ l3_lattices(X0)
| ~ v10_lattices(X4)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != X4 )
| ( k22_filter_2(X0,X1,X2) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_79]) ).
tcf(c_1228,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| m1_subset_1(k22_filter_2(X1,X0,X2),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(unflattening,[status(thm)],[c_1227]) ).
tcf(c_1292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r1_lattices(X1,X2,X3)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ l3_lattices(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r3_lattices(X1,X2,X3)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_112]) ).
tcf(c_1293,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_lattices(X0,X1,X2)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_1292]) ).
tcf(c_1295,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_lattices(X0,X1,X2)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_1293,c_60,c_59,c_57,c_112]) ).
tcf(c_1346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X1)
| v3_struct_0(X0)
| r3_lattices(X0,X2,X2)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ l3_lattices(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_115,c_57]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X0)
| ~ v9_lattices(X1)
| ~ v8_lattices(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(unflattening,[status(thm)],[c_1346]) ).
tcf(c_1365,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X1)
| r3_lattices(X1,X0,X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X0,u1_struct_0(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1347,c_60,c_59]) ).
tcf(c_1417,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(u1_struct_0(X1))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1163,c_86]) ).
tcf(c_1418,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(unflattening,[status(thm)],[c_1417]) ).
tcf(c_1552,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X1,X1)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_1365]) ).
tcf(c_1553,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,X0,X0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1552]) ).
tcf(c_1555,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r3_lattices(sK0,X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1553,c_53,c_51,c_1553]) ).
tcf(c_1556,plain,
! [X0: $i,X1: $i] :
( r3_lattices(sK0,X0,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1555]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| m1_subset_1(k22_filter_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_1228]) ).
tcf(c_1568,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| m1_subset_1(k22_filter_2(sK0,X0,X1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1567]) ).
tcf(c_1570,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| m1_subset_1(k22_filter_2(sK0,X0,X1),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_1568,c_53,c_51,c_1568]) ).
tcf(c_1571,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(k22_filter_2(sK0,X0,X1),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(renaming,[status(thm)],[c_1570]) ).
tcf(c_1582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X1,X3)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X2,X3)
| ~ r2_hidden(X1,k22_filter_2(X0,X2,X3))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_125]) ).
tcf(c_1583,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,X0,X2)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(unflattening,[status(thm)],[c_1582]) ).
tcf(c_1584,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2))
| r3_lattices(sK0,X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_1583,c_53,c_51,c_1583]) ).
tcf(c_1585,plain,
! [X0: $i,X1: $i,X2: $i] :
( r3_lattices(sK0,X0,X2)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(renaming,[status(thm)],[c_1584]) ).
tcf(c_1604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r3_lattices(X0,X2,X1)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X2,X3)
| ~ r2_hidden(X1,k22_filter_2(X0,X2,X3))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_124]) ).
tcf(c_1605,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| r3_lattices(sK0,X1,X0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(unflattening,[status(thm)],[c_1604]) ).
tcf(c_1606,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2))
| r3_lattices(sK0,X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1605,c_53,c_51,c_1605]) ).
tcf(c_1607,plain,
! [X0: $i,X1: $i,X2: $i] :
( r3_lattices(sK0,X1,X0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(renaming,[status(thm)],[c_1606]) ).
tcf(c_1642,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| r1_lattices(X0,X1,X2)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X1,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_1295]) ).
tcf(c_1643,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| r1_lattices(sK0,X0,X1)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_1642]) ).
tcf(c_1645,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,X1)
| r1_lattices(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1643,c_53,c_51,c_1643]) ).
tcf(c_1646,plain,
! [X0: $i,X1: $i] :
( r1_lattices(sK0,X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X0,X1) ),
inference(renaming,[status(thm)],[c_1645]) ).
tcf(c_1674,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ( X1 = X2 )
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r1_lattices(X0,X2,X1)
| ~ r1_lattices(X0,X1,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_1185]) ).
tcf(c_1675,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| ( X0 = X1 )
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r1_lattices(sK0,X1,X0)
| ~ r1_lattices(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_1674]) ).
tcf(c_1677,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r1_lattices(sK0,X1,X0)
| ~ r1_lattices(sK0,X0,X1)
| ( X0 = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_1675,c_53,c_51,c_1675]) ).
tcf(c_1678,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r1_lattices(sK0,X1,X0)
| ~ r1_lattices(sK0,X0,X1) ),
inference(renaming,[status(thm)],[c_1677]) ).
tcf(c_1695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X0)
| r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ l3_lattices(X0)
| ~ m1_subset_1(X3,u1_struct_0(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| ~ r3_lattices(X0,X1,X2)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_123]) ).
tcf(c_1696,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(sK0)
| r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_1695]) ).
tcf(c_1698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1)
| r2_hidden(X2,k22_filter_2(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1696,c_53,c_51,c_1696]) ).
tcf(c_1699,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ m1_subset_1(X2,u1_struct_0(sK0))
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(renaming,[status(thm)],[c_1698]) ).
tcf(c_1729,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ~ l3_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ v1_xboole_0(k22_filter_2(X0,X1,X2))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_72]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ v1_xboole_0(k22_filter_2(sK0,X0,X1)) ),
inference(unflattening,[status(thm)],[c_1729]) ).
tcf(c_1732,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| ~ v1_xboole_0(k22_filter_2(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1730,c_53,c_51,c_1730]) ).
tcf(c_1788,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_1418]) ).
tcf(c_1789,plain,
( v3_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(unflattening,[status(thm)],[c_1788]) ).
tcf(c_1790,plain,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_1789,c_53,c_51,c_137,c_139,c_151]) ).
tcf(c_2911,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ m1_subset_1(X0,u1_struct_0(sK0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_1556]) ).
tcf(c_2912,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ m1_subset_1(X0,u1_struct_0(sK0))
| r3_lattices(sK0,X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_1556]) ).
tcf(c_2913,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1556]) ).
tcf(c_2916,definition,
iPr_def_14 = k1_zfmisc_1(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2919,definition,
iPr_def_17 = k22_filter_2(sK0,sK1,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_2920,definition,
iPr_def_18 = k6_domain_1(iPr_def_13,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_2923,plain,
~ v1_xboole_0(iPr_def_13),
inference(demodulation,[status(thm)],[c_1790]) ).
tcf(c_2924,plain,
! [X0: $i,X1: $i] :
( ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ v1_xboole_0(k22_filter_2(sK0,X0,X1)) ),
inference(demodulation,[status(thm)],[c_1732]) ).
tcf(c_2926,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X2,k22_filter_2(sK0,X0,X1))
| ~ m1_subset_1(X2,iPr_def_13)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X2,X1)
| ~ r3_lattices(sK0,X0,X2)
| ~ r3_lattices(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_1699]) ).
tcf(c_2927,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r1_lattices(sK0,X1,X0)
| ~ r1_lattices(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_1678]) ).
tcf(c_2930,plain,
! [X0: $i,X1: $i] :
( r1_lattices(sK0,X0,X1)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_1646]) ).
tcf(c_2932,plain,
! [X0: $i,X1: $i,X2: $i] :
( r3_lattices(sK0,X1,X0)
| ~ m1_subset_1(X2,iPr_def_13)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(demodulation,[status(thm)],[c_1607]) ).
tcf(c_2933,plain,
! [X0: $i,X1: $i,X2: $i] :
( r3_lattices(sK0,X0,X2)
| ~ m1_subset_1(X2,iPr_def_13)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,X1,X2)
| ~ r2_hidden(X0,k22_filter_2(sK0,X1,X2)) ),
inference(demodulation,[status(thm)],[c_1585]) ).
tcf(c_2934,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(k22_filter_2(sK0,X0,X1),iPr_def_14)
| ~ m1_subset_1(X1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_1571]) ).
tcf(c_2935,plain,
( iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_2913]) ).
tcf(c_2936,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,X0)
| ~ iPr_def_11
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2912]) ).
tcf(c_2937,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_2911]) ).
tcf(c_2939,negated_conjecture,
m1_subset_1(sK1,iPr_def_13),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_2940,negated_conjecture,
~ r1_filter_2(iPr_def_13,iPr_def_17,iPr_def_18),
inference(demodulation,[status(thm)],[c_49,c_2920,c_2919]) ).
tcf(c_2974,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,X0)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_2936,c_2935,c_2936,c_2937]) ).
tcf(c_3879,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,X0)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_2936,c_2974]) ).
tcf(c_4083,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,sK1)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,sK1) ),
inference(superposition,[status(thm)],[c_2919,c_2933]) ).
tcf(c_4084,plain,
! [X0: $i] :
( r3_lattices(sK0,sK1,X0)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,sK1) ),
inference(superposition,[status(thm)],[c_2919,c_2932]) ).
tcf(c_4086,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,sK1)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,sK1) ),
inference(superposition,[status(thm)],[c_2919,c_2926]) ).
tcf(c_4087,plain,
( m1_subset_1(iPr_def_17,iPr_def_14)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2919,c_2934]) ).
tcf(c_4088,plain,
( ~ v1_xboole_0(iPr_def_17)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2919,c_2924]) ).
tcf(c_4089,plain,
~ v1_xboole_0(iPr_def_17),
inference(forward_subsumption_resolution,[status(thm)],[c_4088,c_2939]) ).
tcf(c_4090,plain,
m1_subset_1(iPr_def_17,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_4087,c_2939]) ).
tcf(c_4091,plain,
! [X0: $i] :
( r3_lattices(sK0,sK1,X0)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4084,c_2939]) ).
tcf(c_4096,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,sK1)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4083,c_2939]) ).
tcf(c_4101,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,sK1)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4086,c_2939]) ).
tcf(c_4227,plain,
! [X0: $i] :
( r3_lattices(sK0,sK1,X0)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_3879,c_4091]) ).
tcf(c_4228,plain,
! [X0: $i] :
( r3_lattices(sK0,sK1,X0)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4227,c_2939]) ).
tcf(c_4242,plain,
! [X0: $i] :
( r1_lattices(sK0,sK1,X0)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4228,c_2930]) ).
tcf(c_4243,plain,
! [X0: $i] :
( r1_lattices(sK0,sK1,X0)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4242,c_2939]) ).
tcf(c_4254,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r1_lattices(sK0,X0,sK1) ),
inference(superposition,[status(thm)],[c_4243,c_2927]) ).
tcf(c_4256,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r1_lattices(sK0,X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4254,c_2939]) ).
tcf(c_4270,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,sK1)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_3879,c_4096]) ).
tcf(c_4272,plain,
! [X0: $i] :
( r3_lattices(sK0,X0,sK1)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4270,c_2939]) ).
tcf(c_4286,plain,
! [X0: $i] :
( r1_lattices(sK0,X0,sK1)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4272,c_2930]) ).
tcf(c_4287,plain,
! [X0: $i] :
( r1_lattices(sK0,X0,sK1)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4286,c_2939]) ).
tcf(c_4298,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r1_lattices(sK0,sK1,X0) ),
inference(superposition,[status(thm)],[c_4287,c_2927]) ).
tcf(c_4300,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r1_lattices(sK0,sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4298,c_2939]) ).
tcf(c_4306,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_4256,c_4243,c_4300]) ).
tcf(c_4376,plain,
( v1_xboole_0(iPr_def_13)
| m1_subset_1(iPr_def_18,k1_zfmisc_1(iPr_def_13))
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2920,c_74]) ).
tcf(c_4380,plain,
( v1_xboole_0(iPr_def_13)
| m1_subset_1(iPr_def_18,iPr_def_14)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_4376,c_2916]) ).
tcf(c_4381,plain,
m1_subset_1(iPr_def_18,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_4380,c_2923,c_2939]) ).
tcf(c_4492,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,sK1) ),
inference(superposition,[status(thm)],[c_3879,c_4101]) ).
tcf(c_4495,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_17)
| ~ m1_subset_1(X0,iPr_def_13)
| ~ r3_lattices(sK0,sK1,X0)
| ~ r3_lattices(sK0,X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4492,c_2939]) ).
tcf(c_4513,plain,
( r2_hidden(sK1,iPr_def_17)
| ~ m1_subset_1(sK1,iPr_def_13)
| ~ r3_lattices(sK0,sK1,sK1) ),
inference(superposition,[status(thm)],[c_3879,c_4495]) ).
tcf(c_4516,plain,
( r2_hidden(sK1,iPr_def_17)
| ~ r3_lattices(sK0,sK1,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4513,c_2939]) ).
tcf(c_4523,plain,
( r2_hidden(sK1,iPr_def_17)
| ~ m1_subset_1(sK1,iPr_def_13) ),
inference(superposition,[status(thm)],[c_3879,c_4516]) ).
tcf(c_4526,plain,
r2_hidden(sK1,iPr_def_17),
inference(forward_subsumption_resolution,[status(thm)],[c_4523,c_2939]) ).
tcf(c_4529,plain,
m1_subset_1(sK1,iPr_def_17),
inference(superposition,[status(thm)],[c_4526,c_117]) ).
tcf(c_4590,plain,
( v1_xboole_0(iPr_def_13)
| ( k6_domain_1(iPr_def_13,sK1) = k1_tarski(sK1) ) ),
inference(superposition,[status(thm)],[c_2939,c_108]) ).
tcf(c_4599,plain,
( v1_xboole_0(iPr_def_17)
| ( k6_domain_1(iPr_def_17,sK1) = k1_tarski(sK1) ) ),
inference(superposition,[status(thm)],[c_4529,c_108]) ).
tcf(c_4600,plain,
k6_domain_1(iPr_def_17,sK1) = k1_tarski(sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_4599,c_4089]) ).
tcf(c_4605,plain,
( v1_xboole_0(iPr_def_13)
| ( k1_tarski(sK1) = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4590,c_2920]) ).
tcf(c_4606,plain,
k1_tarski(sK1) = iPr_def_18,
inference(forward_subsumption_resolution,[status(thm)],[c_4605,c_2923]) ).
tcf(c_4860,plain,
k6_domain_1(iPr_def_17,sK1) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_4600,c_4606]) ).
tcf(c_4861,plain,
( v1_xboole_0(iPr_def_17)
| m1_subset_1(iPr_def_18,k1_zfmisc_1(iPr_def_17))
| ~ m1_subset_1(sK1,iPr_def_17) ),
inference(superposition,[status(thm)],[c_4860,c_74]) ).
tcf(c_4862,plain,
m1_subset_1(iPr_def_18,k1_zfmisc_1(iPr_def_17)),
inference(forward_subsumption_resolution,[status(thm)],[c_4861,c_4089,c_4529]) ).
tcf(c_4864,plain,
! [X0: $i] :
( m1_subset_1(X0,iPr_def_17)
| ~ r2_hidden(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_4862,c_121]) ).
tcf(c_4910,plain,
r2_hidden(sK1,iPr_def_18),
inference(superposition,[status(thm)],[c_4606,c_70]) ).
tcf(c_5476,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| r1_filter_2(X0,iPr_def_17,X1)
| r2_hidden(sK2(X0,iPr_def_17,X1),X1)
| ( sK2(X0,iPr_def_17,X1) = sK1 )
| ~ m1_subset_1(iPr_def_17,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| ~ m1_subset_1(sK2(X0,iPr_def_17,X1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_64,c_4306]) ).
tcf(c_5928,plain,
! [X0: $i] :
( v1_xboole_0(iPr_def_13)
| r1_filter_2(iPr_def_13,iPr_def_17,X0)
| r2_hidden(sK2(iPr_def_13,iPr_def_17,X0),X0)
| ( sK2(iPr_def_13,iPr_def_17,X0) = sK1 )
| ~ m1_subset_1(iPr_def_17,k1_zfmisc_1(iPr_def_13))
| ~ m1_subset_1(X0,k1_zfmisc_1(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_65,c_5476]) ).
tcf(c_5929,plain,
! [X0: $i] :
( v1_xboole_0(iPr_def_13)
| r1_filter_2(iPr_def_13,iPr_def_17,X0)
| r2_hidden(sK2(iPr_def_13,iPr_def_17,X0),X0)
| ( sK2(iPr_def_13,iPr_def_17,X0) = sK1 )
| ~ m1_subset_1(iPr_def_17,iPr_def_14)
| ~ m1_subset_1(X0,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_5928,c_2916]) ).
tcf(c_5930,plain,
! [X0: $i] :
( r1_filter_2(iPr_def_13,iPr_def_17,X0)
| r2_hidden(sK2(iPr_def_13,iPr_def_17,X0),X0)
| ( sK2(iPr_def_13,iPr_def_17,X0) = sK1 )
| ~ m1_subset_1(X0,iPr_def_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5929,c_2923,c_4090]) ).
tcf(c_5954,plain,
( r1_filter_2(iPr_def_13,iPr_def_17,iPr_def_18)
| m1_subset_1(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_17)
| ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 )
| ~ m1_subset_1(iPr_def_18,iPr_def_14) ),
inference(superposition,[status(thm)],[c_5930,c_4864]) ).
tcf(c_5962,plain,
( m1_subset_1(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_17)
| ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5954,c_2940,c_4381]) ).
tcf(c_6026,plain,
( v1_xboole_0(iPr_def_17)
| r2_hidden(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_17)
| ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 ) ),
inference(superposition,[status(thm)],[c_5962,c_119]) ).
tcf(c_6027,plain,
( r2_hidden(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_17)
| ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6026,c_4089]) ).
tcf(c_6044,plain,
( r1_filter_2(iPr_def_13,iPr_def_17,iPr_def_18)
| ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 )
| ~ m1_subset_1(iPr_def_18,k1_zfmisc_1(iPr_def_13))
| ~ m1_subset_1(iPr_def_17,k1_zfmisc_1(iPr_def_13))
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_18) ),
inference(superposition,[status(thm)],[c_6027,c_341]) ).
tcf(c_6050,plain,
( r1_filter_2(iPr_def_13,iPr_def_17,iPr_def_18)
| ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 )
| ~ m1_subset_1(iPr_def_18,iPr_def_14)
| ~ m1_subset_1(iPr_def_17,iPr_def_14)
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_18) ),
inference(light_normalisation,[status(thm)],[c_6044,c_2916]) ).
tcf(c_6051,plain,
( ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 )
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6050,c_2940,c_4381,c_4090]) ).
tcf(c_6082,plain,
( r1_filter_2(iPr_def_13,iPr_def_17,iPr_def_18)
| ( sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1 )
| ~ m1_subset_1(iPr_def_18,iPr_def_14) ),
inference(superposition,[status(thm)],[c_5930,c_6051]) ).
tcf(c_6083,plain,
sK2(iPr_def_13,iPr_def_17,iPr_def_18) = sK1,
inference(forward_subsumption_resolution,[status(thm)],[c_6082,c_2940,c_4381]) ).
tcf(c_6287,plain,
( r1_filter_2(iPr_def_13,iPr_def_17,iPr_def_18)
| ~ r2_hidden(sK1,iPr_def_17)
| ~ m1_subset_1(iPr_def_18,k1_zfmisc_1(iPr_def_13))
| ~ m1_subset_1(iPr_def_17,k1_zfmisc_1(iPr_def_13))
| ~ r2_hidden(sK2(iPr_def_13,iPr_def_17,iPr_def_18),iPr_def_18) ),
inference(superposition,[status(thm)],[c_6083,c_341]) ).
tcf(c_6290,plain,
( r1_filter_2(iPr_def_13,iPr_def_17,iPr_def_18)
| ~ r2_hidden(sK1,iPr_def_18)
| ~ r2_hidden(sK1,iPr_def_17)
| ~ m1_subset_1(iPr_def_18,iPr_def_14)
| ~ m1_subset_1(iPr_def_17,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_6287,c_2916,c_6083]) ).
tcf(c_6291,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6290,c_2940,c_4910,c_4526,c_4381,c_4090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT328+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 21:12:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/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...
% 3.77/1.20 % SZS status Started for theBenchmark.p
% 3.77/1.20 % SZS status Theorem for theBenchmark.p
% 3.77/1.20
% 3.77/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.77/1.20
% 3.77/1.20 % ------ iProver source info
% 3.77/1.20
% 3.77/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.77/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.77/1.20 % git: non_committed_changes: false
% 3.77/1.20
% 3.77/1.20 % ------ Parsing...
% 3.77/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.77/1.20
% 3.77/1.20 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 3.77/1.20
% 3.77/1.20 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.77/1.20
% 3.77/1.20 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 3.77/1.20 % ------ Proving...
% 3.77/1.20 % ------ Problem Properties
% 3.77/1.20
% 3.77/1.20 %
% 3.77/1.20 % clauses 80
% 3.77/1.20 % conjectures 3
% 3.77/1.20 % EPR 28
% 3.77/1.20 % Horn 65
% 3.77/1.20 % unary 34
% 3.77/1.20 % binary 21
% 3.77/1.20 % lits 180
% 3.77/1.20 % lits eq 19
% 3.77/1.20 % fd_pure 0
% 3.77/1.20 % fd_pseudo 0
% 3.77/1.20 % fd_cond 1
% 3.77/1.20 % fd_pseudo_cond 5
% 3.77/1.20 % AC symbols 0
% 3.77/1.20
% 3.77/1.20 % ------ Schedule dynamic 5 is on
% 3.77/1.20
% 3.77/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.77/1.20
% 3.77/1.20
% 3.77/1.20 % ------
% 3.77/1.20 % Current options:
% 3.77/1.20 % ------
% 3.77/1.20
% 3.77/1.20
% 3.77/1.20 %
% 3.77/1.20
% 3.77/1.20 % ------ Proving...
% 3.77/1.20 %
% 3.77/1.20
% 3.77/1.20 % SZS status Theorem for theBenchmark.p
% 3.77/1.20
% 3.77/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.35/1.20
% 1.35/1.20
%------------------------------------------------------------------------------