TSTP Solution File: LAT311+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LAT311+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:35:13 EDT 2024
% Result : Theorem 184.50s 25.27s
% Output : CNFRefutation 184.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 25
% Syntax : Number of formulae : 169 ( 23 unt; 0 def)
% Number of atoms : 744 ( 121 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 947 ( 372 ~; 394 |; 146 &)
% ( 1 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-2 aty)
% Number of variables : 250 ( 2 sgn 140 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [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,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
=> ( r2_hidden(X1,X2)
=> r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_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))
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
=> ( r2_hidden(X1,X2)
=> r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2)) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f12,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k5_filter_2(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).
fof(f13,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> k7_filter_2(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).
fof(f15,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).
fof(f19,axiom,
! [X0] :
( l3_lattices(X0)
=> ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(f27,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(f28,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).
fof(f55,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1)
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(k7_filter_2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_2) ).
fof(f67,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(f84,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,u1_struct_0(X0))
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k2_filter_0(X0,X1) = k2_filter_2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).
fof(f85,axiom,
! [X0,X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1)
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> k3_filter_0(X0,X1) = k3_filter_2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).
fof(f92,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,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
=> ( r2_hidden(X1,X2)
=> r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).
fof(f95,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ( k2_filter_2(X0,X1) = k18_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
& k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).
fof(f96,axiom,
! [X0] :
( ( l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X1) )
=> ! [X2] :
( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
& ~ v1_xboole_0(X2) )
=> ( k3_filter_2(k1_lattice2(X0),X2) = k19_filter_2(X0,k8_filter_2(X0,X2))
& k3_filter_2(X0,k8_filter_2(X0,X2)) = k19_filter_2(k1_lattice2(X0),X2)
& k3_filter_2(X0,X1) = k19_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
& k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).
fof(f97,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f98,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f101,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f114,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2))
& r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
& m1_subset_1(X1,u1_struct_0(X0)) )
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f115,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2))
& r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
& m1_subset_1(X1,u1_struct_0(X0)) )
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) ),
inference(flattening,[],[f114]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( k5_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( k5_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( k7_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( k7_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f132]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f136]) ).
fof(f144,plain,
! [X0] :
( ( l3_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0)) )
| ~ l3_lattices(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f153,plain,
! [X0,X1] :
( m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0)))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f154,plain,
! [X0,X1] :
( m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0)))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0,X1] :
( m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f156,plain,
! [X0,X1] :
( m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f155]) ).
fof(f181,plain,
! [X0,X1] :
( ~ v1_xboole_0(k7_filter_2(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f182,plain,
! [X0,X1] :
( ~ v1_xboole_0(k7_filter_2(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f181]) ).
fof(f201,plain,
! [X0] :
( ( v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f202,plain,
! [X0] :
( ( v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f201]) ).
fof(f214,plain,
! [X0,X1] :
( k2_filter_0(X0,X1) = k2_filter_2(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f215,plain,
! [X0,X1] :
( k2_filter_0(X0,X1) = k2_filter_2(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f214]) ).
fof(f216,plain,
! [X0,X1] :
( k3_filter_0(X0,X1) = k3_filter_2(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f217,plain,
! [X0,X1] :
( k3_filter_0(X0,X1) = k3_filter_2(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f216]) ).
fof(f225,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2))
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X2) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f226,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2))
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X2) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f225]) ).
fof(f230,plain,
! [X0] :
( ! [X1] :
( ( k2_filter_2(X0,X1) = k18_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
& k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( k2_filter_2(X0,X1) = k18_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
& k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f230]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k3_filter_2(k1_lattice2(X0),X2) = k19_filter_2(X0,k8_filter_2(X0,X2))
& k3_filter_2(X0,k8_filter_2(X0,X2)) = k19_filter_2(k1_lattice2(X0),X2)
& k3_filter_2(X0,X1) = k19_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
& k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1)) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| v1_xboole_0(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k3_filter_2(k1_lattice2(X0),X2) = k19_filter_2(X0,k8_filter_2(X0,X2))
& k3_filter_2(X0,k8_filter_2(X0,X2)) = k19_filter_2(k1_lattice2(X0),X2)
& k3_filter_2(X0,X1) = k19_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
& k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1)) )
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| v1_xboole_0(X2) )
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1) )
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f232]) ).
fof(f234,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f98]) ).
fof(f235,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(flattening,[],[f234]) ).
fof(f238,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f101]) ).
fof(f240,plain,
! [X0] :
( ( v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f241,plain,
! [X0] :
( sP0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(definition_folding,[],[f202,f240]) ).
fof(f242,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2))
& r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& ~ v1_xboole_0(X2) )
& m1_subset_1(X1,u1_struct_0(X0)) )
& l3_lattices(X0)
& v10_lattices(X0)
& ~ v3_struct_0(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ r1_tarski(k18_filter_2(sK1,X1),k19_filter_2(sK1,X2))
& r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v1_xboole_0(X2) )
& m1_subset_1(X1,u1_struct_0(sK1)) )
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f243,plain,
( ? [X1] :
( ? [X2] :
( ~ r1_tarski(k18_filter_2(sK1,X1),k19_filter_2(sK1,X2))
& r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v1_xboole_0(X2) )
& m1_subset_1(X1,u1_struct_0(sK1)) )
=> ( ? [X2] :
( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,X2))
& r2_hidden(sK2,X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v1_xboole_0(X2) )
& m1_subset_1(sK2,u1_struct_0(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f244,plain,
( ? [X2] :
( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,X2))
& r2_hidden(sK2,X2)
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v1_xboole_0(X2) )
=> ( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3))
& r2_hidden(sK2,sK3)
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v1_xboole_0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f245,plain,
( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3))
& r2_hidden(sK2,sK3)
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
& ~ v1_xboole_0(sK3)
& m1_subset_1(sK2,u1_struct_0(sK1))
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f115,f244,f243,f242]) ).
fof(f268,plain,
! [X0] :
( ( v10_lattices(k1_lattice2(X0))
& v9_lattices(k1_lattice2(X0))
& v8_lattices(k1_lattice2(X0))
& v7_lattices(k1_lattice2(X0))
& v6_lattices(k1_lattice2(X0))
& v5_lattices(k1_lattice2(X0))
& v4_lattices(k1_lattice2(X0))
& v3_lattices(k1_lattice2(X0))
& ~ v3_struct_0(k1_lattice2(X0)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f240]) ).
fof(f309,plain,
! [X0,X1] :
( ( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
& ( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f97]) ).
fof(f310,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f245]) ).
fof(f311,plain,
v10_lattices(sK1),
inference(cnf_transformation,[],[f245]) ).
fof(f312,plain,
l3_lattices(sK1),
inference(cnf_transformation,[],[f245]) ).
fof(f313,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f245]) ).
fof(f314,plain,
~ v1_xboole_0(sK3),
inference(cnf_transformation,[],[f245]) ).
fof(f315,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f245]) ).
fof(f316,plain,
r2_hidden(sK2,sK3),
inference(cnf_transformation,[],[f245]) ).
fof(f317,plain,
~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)),
inference(cnf_transformation,[],[f245]) ).
fof(f335,plain,
! [X0,X1] :
( k5_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f336,plain,
! [X0,X1] :
( k7_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f338,plain,
! [X0,X1] :
( k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f344,plain,
! [X0] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f349,plain,
! [X0,X1] :
( m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0)))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f350,plain,
! [X0,X1] :
( m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f381,plain,
! [X0,X1] :
( ~ v1_xboole_0(k7_filter_2(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f403,plain,
! [X0] :
( ~ v3_struct_0(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f411,plain,
! [X0] :
( v10_lattices(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f412,plain,
! [X0] :
( sP0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f458,plain,
! [X0,X1] :
( k2_filter_0(X0,X1) = k2_filter_2(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f459,plain,
! [X0,X1] :
( k3_filter_0(X0,X1) = k3_filter_2(X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f469,plain,
! [X2,X0,X1] :
( r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2))
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f473,plain,
! [X0,X1] :
( k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f475,plain,
! [X2,X0,X1] :
( k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f479,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f309]) ).
fof(f480,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f309]) ).
fof(f481,plain,
! [X2,X0,X1] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f235]) ).
fof(f484,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
cnf(c_49,negated_conjecture,
~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)),
inference(cnf_transformation,[],[f317]) ).
cnf(c_50,negated_conjecture,
r2_hidden(sK2,sK3),
inference(cnf_transformation,[],[f316]) ).
cnf(c_51,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f315]) ).
cnf(c_52,negated_conjecture,
~ v1_xboole_0(sK3),
inference(cnf_transformation,[],[f314]) ).
cnf(c_53,negated_conjecture,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f313]) ).
cnf(c_54,negated_conjecture,
l3_lattices(sK1),
inference(cnf_transformation,[],[f312]) ).
cnf(c_55,negated_conjecture,
v10_lattices(sK1),
inference(cnf_transformation,[],[f311]) ).
cnf(c_56,negated_conjecture,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f310]) ).
cnf(c_70,plain,
( ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k5_filter_2(X1,X0) = X0
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f335]) ).
cnf(c_71,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k7_filter_2(X1,X0) = X0
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f336]) ).
cnf(c_73,plain,
( ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k18_filter_2(X1,X0) = a_2_0_filter_2(X1,X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f338]) ).
cnf(c_78,plain,
( ~ l3_lattices(X0)
| l3_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f344]) ).
cnf(c_84,plain,
( ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(k5_filter_2(X1,X0),u1_struct_0(k1_lattice2(X1)))
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f349]) ).
cnf(c_85,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| m1_subset_1(k7_filter_2(X1,X0),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f350]) ).
cnf(c_116,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_xboole_0(k7_filter_2(X1,X0))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v1_xboole_0(X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f381]) ).
cnf(c_138,plain,
( ~ sP0(X0)
| v10_lattices(k1_lattice2(X0)) ),
inference(cnf_transformation,[],[f411]) ).
cnf(c_146,plain,
( ~ v3_struct_0(k1_lattice2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f403]) ).
cnf(c_147,plain,
( ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f412]) ).
cnf(c_193,plain,
( ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k2_filter_0(X1,X0) = k2_filter_2(X1,X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f458]) ).
cnf(c_194,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k3_filter_0(X1,X0) = k3_filter_2(X1,X0)
| v1_xboole_0(X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f459]) ).
cnf(c_204,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X2,X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X0))
| v1_xboole_0(X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f469]) ).
cnf(c_209,plain,
( ~ m1_subset_1(X0,u1_struct_0(X1))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X0)) = k18_filter_2(X1,X0)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f473]) ).
cnf(c_213,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2)
| v1_xboole_0(X0)
| v1_xboole_0(X2)
| v3_struct_0(X1) ),
inference(cnf_transformation,[],[f475]) ).
cnf(c_214,plain,
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[],[f480]) ).
cnf(c_215,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f479]) ).
cnf(c_216,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r2_hidden(X2,X0)
| m1_subset_1(X2,X1) ),
inference(cnf_transformation,[],[f481]) ).
cnf(c_219,plain,
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f484]) ).
cnf(c_354,plain,
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(prop_impl_just,[status(thm)],[c_215]) ).
cnf(c_355,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(renaming,[status(thm)],[c_354]) ).
cnf(c_356,plain,
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(prop_impl_just,[status(thm)],[c_214]) ).
cnf(c_372,plain,
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) ),
inference(prop_impl_just,[status(thm)],[c_219]) ).
cnf(c_698,plain,
( ~ r1_tarski(X0,X1)
| ~ r2_hidden(X2,X0)
| m1_subset_1(X2,X1) ),
inference(bin_hyper_res,[status(thm)],[c_216,c_356]) ).
cnf(c_868,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ r2_hidden(X2,X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X0))
| v3_struct_0(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_204,c_372]) ).
cnf(c_3684,plain,
( X0 != X1
| X2 != X3
| ~ m1_subset_1(X0,k1_zfmisc_1(X2))
| ~ r2_hidden(X4,X1)
| m1_subset_1(X4,X3) ),
inference(resolution_lifted,[status(thm)],[c_355,c_698]) ).
cnf(c_3685,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r2_hidden(X2,X0)
| m1_subset_1(X2,X1) ),
inference(unflattening,[status(thm)],[c_3684]) ).
cnf(c_3816,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X2,X0)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X0))
| v3_struct_0(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_868,c_3685]) ).
cnf(c_4828,plain,
( X0 != sK1
| ~ l3_lattices(X0)
| v3_struct_0(X0)
| sP0(X0) ),
inference(resolution_lifted,[status(thm)],[c_55,c_147]) ).
cnf(c_4829,plain,
( ~ l3_lattices(sK1)
| v3_struct_0(sK1)
| sP0(sK1) ),
inference(unflattening,[status(thm)],[c_4828]) ).
cnf(c_13348,plain,
X0 = X0,
theory(equality) ).
cnf(c_13350,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_13353,plain,
( X0 != X1
| X2 != X3
| ~ r1_tarski(X1,X3)
| r1_tarski(X0,X2) ),
theory(equality) ).
cnf(c_13354,plain,
( X0 != X1
| X2 != X3
| ~ r2_hidden(X1,X3)
| r2_hidden(X0,X2) ),
theory(equality) ).
cnf(c_16610,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| k5_filter_2(sK1,sK2) = sK2
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_16615,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| k7_filter_2(sK1,sK3) = sK3
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_16662,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| m1_subset_1(k5_filter_2(sK1,sK2),u1_struct_0(k1_lattice2(sK1)))
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[c_84]) ).
cnf(c_16670,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[c_85]) ).
cnf(c_16800,plain,
( X0 != sK2
| X1 != sK3
| ~ r2_hidden(sK2,sK3)
| r2_hidden(X0,X1) ),
inference(instantiation,[status(thm)],[c_13354]) ).
cnf(c_16871,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| k18_filter_2(sK1,sK2) = a_2_0_filter_2(sK1,sK2)
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_16964,plain,
( ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) = k18_filter_2(sK1,sK2)
| v3_struct_0(sK1) ),
inference(instantiation,[status(thm)],[c_209]) ).
cnf(c_17269,plain,
( ~ m1_subset_1(k5_filter_2(sK1,sK2),u1_struct_0(k1_lattice2(sK1)))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) = k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(instantiation,[status(thm)],[c_193]) ).
cnf(c_17301,plain,
( ~ m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) = k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
| v1_xboole_0(k7_filter_2(sK1,sK3))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(instantiation,[status(thm)],[c_194]) ).
cnf(c_17464,plain,
k19_filter_2(sK1,sK3) = k19_filter_2(sK1,sK3),
inference(instantiation,[status(thm)],[c_13348]) ).
cnf(c_17466,plain,
( k19_filter_2(sK1,sK3) != X0
| X1 != X0
| k19_filter_2(sK1,sK3) = X1 ),
inference(instantiation,[status(thm)],[c_13350]) ).
cnf(c_17501,plain,
( k5_filter_2(sK1,sK2) != sK2
| X0 != sK3
| ~ r2_hidden(sK2,sK3)
| r2_hidden(k5_filter_2(sK1,sK2),X0) ),
inference(instantiation,[status(thm)],[c_16800]) ).
cnf(c_19101,plain,
( ~ v1_xboole_0(k7_filter_2(sK1,sK3))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v1_xboole_0(sK3)
| v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_51,c_116]) ).
cnf(c_19113,plain,
~ v1_xboole_0(k7_filter_2(sK1,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_19101,c_56,c_52,c_55,c_54]) ).
cnf(c_22019,plain,
( ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| k7_filter_2(sK1,sK3) = sK3
| v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_51,c_71]) ).
cnf(c_22030,plain,
k7_filter_2(sK1,sK3) = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_22019,c_56,c_55,c_54]) ).
cnf(c_22270,plain,
( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
| v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_22030,c_85]) ).
cnf(c_22279,plain,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_22270,c_56,c_55,c_54,c_51]) ).
cnf(c_22853,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,X0)) = k19_filter_2(sK1,X0)
| v1_xboole_0(X0)
| v1_xboole_0(sK3)
| v3_struct_0(sK1) ),
inference(superposition,[status(thm)],[c_22279,c_213]) ).
cnf(c_22854,plain,
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
| k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,X0)) = k19_filter_2(sK1,X0)
| v1_xboole_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22853,c_56,c_52,c_55,c_54]) ).
cnf(c_23023,plain,
( ~ sP0(sK1)
| v10_lattices(k1_lattice2(sK1)) ),
inference(instantiation,[status(thm)],[c_138]) ).
cnf(c_23476,plain,
( k18_filter_2(sK1,sK2) != X0
| X1 != X0
| X1 = k18_filter_2(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_13350]) ).
cnf(c_23528,plain,
( k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) = k19_filter_2(sK1,sK3)
| v1_xboole_0(sK3) ),
inference(superposition,[status(thm)],[c_51,c_22854]) ).
cnf(c_23540,plain,
k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) = k19_filter_2(sK1,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_23528,c_52]) ).
cnf(c_24291,plain,
( k5_filter_2(sK1,sK2) != sK2
| k7_filter_2(sK1,sK3) != sK3
| ~ r2_hidden(sK2,sK3)
| r2_hidden(k5_filter_2(sK1,sK2),k7_filter_2(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_17501]) ).
cnf(c_24435,plain,
( ~ l3_lattices(sK1)
| l3_lattices(k1_lattice2(sK1)) ),
inference(instantiation,[status(thm)],[c_78]) ).
cnf(c_25044,plain,
( k19_filter_2(sK1,sK3) != k19_filter_2(sK1,sK3)
| X0 != k19_filter_2(sK1,sK3)
| k19_filter_2(sK1,sK3) = X0 ),
inference(instantiation,[status(thm)],[c_17466]) ).
cnf(c_35093,plain,
( ~ v3_struct_0(k1_lattice2(sK1))
| ~ sP0(sK1) ),
inference(instantiation,[status(thm)],[c_146]) ).
cnf(c_38170,plain,
( k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) != k19_filter_2(sK1,sK3)
| k19_filter_2(sK1,sK3) != k19_filter_2(sK1,sK3)
| k19_filter_2(sK1,sK3) = k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_25044]) ).
cnf(c_39008,plain,
( k19_filter_2(sK1,sK3) != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
| X0 != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
| k19_filter_2(sK1,sK3) = X0 ),
inference(instantiation,[status(thm)],[c_17466]) ).
cnf(c_43163,plain,
( k18_filter_2(sK1,sK2) != a_2_0_filter_2(sK1,sK2)
| X0 != a_2_0_filter_2(sK1,sK2)
| X0 = k18_filter_2(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_23476]) ).
cnf(c_50585,plain,
( k18_filter_2(sK1,sK2) != a_2_0_filter_2(sK1,sK2)
| k18_filter_2(sK1,sK2) = k18_filter_2(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_43163]) ).
cnf(c_52734,plain,
( k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
| k19_filter_2(sK1,sK3) != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
| k19_filter_2(sK1,sK3) = k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_39008]) ).
cnf(c_81083,plain,
( ~ m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(X0)))
| ~ r2_hidden(k5_filter_2(sK1,sK2),k7_filter_2(sK1,sK3))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| r1_tarski(k2_filter_0(X0,k5_filter_2(sK1,sK2)),k3_filter_0(X0,k7_filter_2(sK1,sK3)))
| v3_struct_0(X0) ),
inference(instantiation,[status(thm)],[c_3816]) ).
cnf(c_121076,plain,
( ~ m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
| ~ r2_hidden(k5_filter_2(sK1,sK2),k7_filter_2(sK1,sK3))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| r1_tarski(k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)),k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(instantiation,[status(thm)],[c_81083]) ).
cnf(c_184009,plain,
( k18_filter_2(sK1,sK2) != X0
| k19_filter_2(sK1,sK3) != X1
| ~ r1_tarski(X0,X1)
| r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_13353]) ).
cnf(c_184876,plain,
( k18_filter_2(sK1,sK2) != X0
| X1 != X0
| k18_filter_2(sK1,sK2) = X1 ),
inference(instantiation,[status(thm)],[c_13350]) ).
cnf(c_188325,plain,
( k18_filter_2(sK1,sK2) != k18_filter_2(sK1,sK2)
| X0 != k18_filter_2(sK1,sK2)
| k18_filter_2(sK1,sK2) = X0 ),
inference(instantiation,[status(thm)],[c_184876]) ).
cnf(c_193519,plain,
( k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) != k18_filter_2(sK1,sK2)
| k18_filter_2(sK1,sK2) != k18_filter_2(sK1,sK2)
| k18_filter_2(sK1,sK2) = k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_188325]) ).
cnf(c_193910,plain,
( k18_filter_2(sK1,sK2) != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
| X0 != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
| k18_filter_2(sK1,sK2) = X0 ),
inference(instantiation,[status(thm)],[c_184876]) ).
cnf(c_198118,plain,
( k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
| k18_filter_2(sK1,sK2) != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
| k18_filter_2(sK1,sK2) = k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_193910]) ).
cnf(c_199918,plain,
( k18_filter_2(sK1,sK2) != X0
| k19_filter_2(sK1,sK3) != k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
| ~ r1_tarski(X0,k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)))
| r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_184009]) ).
cnf(c_280529,plain,
( k18_filter_2(sK1,sK2) != k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
| k19_filter_2(sK1,sK3) != k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
| ~ r1_tarski(k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)),k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)))
| r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)) ),
inference(instantiation,[status(thm)],[c_199918]) ).
cnf(c_280530,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_280529,c_198118,c_193519,c_121076,c_52734,c_50585,c_38170,c_35093,c_24435,c_24291,c_23540,c_23023,c_19113,c_17464,c_17301,c_17269,c_16964,c_16871,c_16670,c_16662,c_16615,c_16610,c_4829,c_49,c_51,c_53,c_50,c_56,c_54,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT311+1 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 18:07:25 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 184.50/25.27 % SZS status Started for theBenchmark.p
% 184.50/25.27 % SZS status Theorem for theBenchmark.p
% 184.50/25.27
% 184.50/25.27 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 184.50/25.27
% 184.50/25.27 ------ iProver source info
% 184.50/25.27
% 184.50/25.27 git: date: 2024-05-02 19:28:25 +0000
% 184.50/25.27 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 184.50/25.27 git: non_committed_changes: false
% 184.50/25.27
% 184.50/25.27 ------ Parsing...
% 184.50/25.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 184.50/25.27
% 184.50/25.27 ------ Preprocessing... sup_sim: 0 sf_s rm: 10 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: 10 0s sf_e pe_s pe_e
% 184.50/25.27
% 184.50/25.27 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 184.50/25.27
% 184.50/25.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 184.50/25.27 ------ Proving...
% 184.50/25.27 ------ Problem Properties
% 184.50/25.27
% 184.50/25.27
% 184.50/25.27 clauses 154
% 184.50/25.27 conjectures 8
% 184.50/25.27 EPR 45
% 184.50/25.27 Horn 98
% 184.50/25.27 unary 48
% 184.50/25.27 binary 36
% 184.50/25.27 lits 484
% 184.50/25.27 lits eq 27
% 184.50/25.27 fd_pure 0
% 184.50/25.27 fd_pseudo 0
% 184.50/25.27 fd_cond 1
% 184.50/25.27 fd_pseudo_cond 6
% 184.50/25.27 AC symbols 0
% 184.50/25.27
% 184.50/25.27 ------ Input Options Time Limit: Unbounded
% 184.50/25.27
% 184.50/25.27
% 184.50/25.27 ------
% 184.50/25.27 Current options:
% 184.50/25.27 ------
% 184.50/25.27
% 184.50/25.27
% 184.50/25.27
% 184.50/25.27
% 184.50/25.27 ------ Proving...
% 184.50/25.27
% 184.50/25.27
% 184.50/25.27 % SZS status Theorem for theBenchmark.p
% 184.50/25.27
% 184.50/25.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 184.50/25.27
% 184.50/25.28
%------------------------------------------------------------------------------