%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT311+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Thu Sep 24 01:02:40 PM UTC 2026
% Result : Theorem 0.30s 1.09s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 152 ( 17 unt; 22 def)
% Number of atoms : 565 ( 50 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 656 ( 243 ~; 278 |; 80 &)
% ( 22 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 23 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-2 aty)
% Number of variables : 117 ( 114 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C) )
=> ( r2_hidden(B,C)
=> r1_tarski(k18_filter_2(A,B),k19_filter_2(A,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C) )
=> ( r2_hidden(B,C)
=> r1_tarski(k18_filter_2(A,B),k19_filter_2(A,C)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f12,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_filter_2(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k7_filter_2(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))
=> k8_filter_2(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( l3_lattices(A)
=> ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( ( m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k5_filter_2(A,B),u1_struct_0(k1_lattice2(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k7_filter_2(A,B),k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v10_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [A,B] :
( ( m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k2_filter_2(A,B) = k2_filter_0(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k3_filter_2(A,B) = k3_filter_0(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C) )
=> ( r2_hidden(B,C)
=> r1_tarski(k2_filter_0(A,B),k3_filter_0(A,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k18_filter_2(k1_lattice2(A),k5_filter_2(A,B)) = k2_filter_2(A,B)
& k18_filter_2(A,B) = k2_filter_2(k1_lattice2(A),k5_filter_2(A,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))
& ~ v1_xboole_0(C) )
=> ( k3_filter_2(k1_lattice2(A),C) = k19_filter_2(A,k8_filter_2(A,C))
& k3_filter_2(A,k8_filter_2(A,C)) = k19_filter_2(k1_lattice2(A),C)
& k3_filter_2(A,B) = k19_filter_2(k1_lattice2(A),k7_filter_2(A,B))
& k3_filter_2(k1_lattice2(A),k7_filter_2(A,B)) = k19_filter_2(A,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ r1_tarski(k18_filter_2(A,B),k19_filter_2(A,C))
& r2_hidden(B,C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C) )
& m1_subset_1(B,u1_struct_0(A)) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f104,plain,
( ~ r1_tarski(k18_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK2_skl))
& r2_hidden(sK1_skl,sK2_skl)
& m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& ~ v1_xboole_0(sK2_skl)
& m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
& l3_lattices(sK0_skl)
& v10_lattices(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f103]) ).
fof(f105,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
v10_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
l3_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f108,plain,
m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f109,plain,
~ v1_xboole_0(sK2_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f110,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f111,plain,
r2_hidden(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f112,plain,
~ r1_tarski(k18_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f141,plain,
! [A] :
( ! [B] :
( k5_filter_2(A,B) = B
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f142,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,[status(thm)],[f141]) ).
fof(f143,plain,
! [A] :
( ! [B] :
( k7_filter_2(A,B) = B
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f144,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,[status(thm)],[f143]) ).
fof(f145,plain,
! [A] :
( ! [B] :
( k8_filter_2(A,B) = B
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f146,plain,
! [X0,X1] :
( k8_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f156,plain,
! [A] :
( ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) )
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f158,plain,
! [X0] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f167,plain,
! [A,B] :
( m1_subset_1(k5_filter_2(A,B),u1_struct_0(k1_lattice2(A)))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f168,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,[status(thm)],[f167]) ).
fof(f169,plain,
! [A,B] :
( m1_subset_1(k7_filter_2(A,B),k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f170,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,[status(thm)],[f169]) ).
fof(f229,plain,
! [A] :
( ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f230,plain,
! [X0] :
( ~ v3_struct_0(k1_lattice2(X0))
| ~ l3_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f267,plain,
! [A] :
( ( v10_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f276,plain,
! [X0] :
( v10_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f348,plain,
! [A,B] :
( k2_filter_2(A,B) = k2_filter_0(A,B)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f349,plain,
! [X0,X1] :
( k2_filter_2(X0,X1) = k2_filter_0(X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f348]) ).
fof(f350,plain,
! [A,B] :
( k3_filter_2(A,B) = k3_filter_0(A,B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f351,plain,
! [X0,X1] :
( k3_filter_2(X0,X1) = k3_filter_0(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,[status(thm)],[f350]) ).
fof(f370,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f371,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f372,plain,
! [A] :
( ! [B] :
( ! [C] :
( r1_tarski(k2_filter_0(A,B),k3_filter_0(A,C))
| ~ r2_hidden(B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(C) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f373,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(cnf_transformation,[status(thm)],[f372]) ).
fof(f374,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f375,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f381,plain,
! [A] :
( ! [B] :
( ( k18_filter_2(k1_lattice2(A),k5_filter_2(A,B)) = k2_filter_2(A,B)
& k18_filter_2(A,B) = k2_filter_2(k1_lattice2(A),k5_filter_2(A,B)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f95]) ).
fof(f382,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,[status(thm)],[f381]) ).
fof(f384,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( k3_filter_2(k1_lattice2(A),C) = k19_filter_2(A,k8_filter_2(A,C))
& k3_filter_2(A,k8_filter_2(A,C)) = k19_filter_2(k1_lattice2(A),C)
& k3_filter_2(A,B) = k19_filter_2(k1_lattice2(A),k7_filter_2(A,B))
& k3_filter_2(k1_lattice2(A),k7_filter_2(A,B)) = k19_filter_2(A,B) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))
| v1_xboole_0(C) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f388,plain,
! [X0,X1,X2] :
( k3_filter_2(k1_lattice2(X0),X2) = k19_filter_2(X0,k8_filter_2(X0,X2))
| ~ 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,[status(thm)],[f384]) ).
fof(f393,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f98]) ).
fof(f394,plain,
! [A,C] :
( m1_subset_1(A,C)
| ! [B] :
( ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ) ),
inference(miniscoping,[status(thm)],[f393]) ).
fof(f395,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f394]) ).
fof(f436,definition,
( sQ6_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ6_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
( sQ7_spl
<=> v10_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ7_spl
| ~ v10_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f446,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f441,f106]) ).
fof(f447,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f446]) ).
fof(f448,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f437,f105]) ).
fof(f449,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f465,plain,
m1_subset_1(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f371,f111]) ).
fof(f467,plain,
( r2_hidden(sK1_skl,sK2_skl)
| v1_xboole_0(sK2_skl) ),
inference(resolution,[status(thm)],[f375,f465]) ).
fof(f476,definition,
( sQ14_spl
<=> v1_xboole_0(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( ~ sQ14_spl
| v1_xboole_0(sK2_skl) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,definition,
( sQ15_spl
<=> r2_hidden(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f467,f476,f479]) ).
fof(f490,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f109]) ).
fof(f491,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f647,definition,
( sQ46_spl
<=> l3_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( sQ46_spl
| ~ l3_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f647]) ).
fof(f681,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f649,f107]) ).
fof(f682,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f697,plain,
( k5_filter_2(sK0_skl,sK1_skl) = sK1_skl
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f142,f108]) ).
fof(f698,definition,
( sQ50_spl
<=> k5_filter_2(sK0_skl,sK1_skl) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( ~ sQ50_spl
| k5_filter_2(sK0_skl,sK1_skl) = sK1_skl ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f701,plain,
( sQ50_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f697,f436,f439,f647,f698]) ).
fof(f702,plain,
( k7_filter_2(sK0_skl,sK2_skl) = sK2_skl
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f144,f110]) ).
fof(f704,definition,
( sQ51_spl
<=> k7_filter_2(sK0_skl,sK2_skl) = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f705,plain,
( ~ sQ51_spl
| k7_filter_2(sK0_skl,sK2_skl) = sK2_skl ),
inference(component_clause,[status(thm)],[f704]) ).
fof(f707,plain,
( sQ51_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f702,f436,f439,f647,f704]) ).
fof(f790,plain,
( ~ sQ50_spl
| m1_subset_1(sK1_skl,u1_struct_0(k1_lattice2(sK0_skl)))
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(paramodulation,[status(thm)],[f699,f168]) ).
fof(f792,definition,
( sQ58_spl
<=> m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f794,plain,
( sQ58_spl
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f792]) ).
fof(f795,definition,
( sQ59_spl
<=> m1_subset_1(sK1_skl,u1_struct_0(k1_lattice2(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f798,plain,
( ~ sQ50_spl
| sQ59_spl
| ~ sQ58_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f790,f436,f439,f647,f792,f795,f698]) ).
fof(f799,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f794,f108]) ).
fof(f800,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f799]) ).
fof(f803,definition,
( sQ60_spl
<=> v3_struct_0(k1_lattice2(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f804,plain,
( ~ sQ60_spl
| v3_struct_0(k1_lattice2(sK0_skl)) ),
inference(component_clause,[status(thm)],[f803]) ).
fof(f806,definition,
( sQ61_spl
<=> v10_lattices(k1_lattice2(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f808,plain,
( sQ61_spl
| ~ v10_lattices(k1_lattice2(sK0_skl)) ),
inference(component_clause,[status(thm)],[f806]) ).
fof(f809,definition,
( sQ62_spl
<=> l3_lattices(k1_lattice2(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f811,plain,
( sQ62_spl
| ~ l3_lattices(k1_lattice2(sK0_skl)) ),
inference(component_clause,[status(thm)],[f809]) ).
fof(f841,plain,
( ~ sQ51_spl
| m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK0_skl))))
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(paramodulation,[status(thm)],[f705,f170]) ).
fof(f848,definition,
( sQ66_spl
<=> m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f850,plain,
( sQ66_spl
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f848]) ).
fof(f851,definition,
( sQ67_spl
<=> m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( ~ sQ67_spl
| m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f851]) ).
fof(f854,plain,
( ~ sQ51_spl
| sQ67_spl
| ~ sQ66_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f841,f436,f439,f647,f848,f851,f704]) ).
fof(f855,plain,
( sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f850,f110]) ).
fof(f856,plain,
sQ66_spl,
inference(contradiction_clause,[status(thm)],[f855]) ).
fof(f873,plain,
( ~ sQ67_spl
| k8_filter_2(sK0_skl,sK2_skl) = sK2_skl
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f852,f146]) ).
fof(f882,definition,
( sQ68_spl
<=> k8_filter_2(sK0_skl,sK2_skl) = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f883,plain,
( ~ sQ68_spl
| k8_filter_2(sK0_skl,sK2_skl) = sK2_skl ),
inference(component_clause,[status(thm)],[f882]) ).
fof(f885,plain,
( ~ sQ67_spl
| sQ68_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f873,f436,f439,f647,f882,f851]) ).
fof(f912,plain,
( sQ62_spl
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f811,f158]) ).
fof(f913,plain,
( sQ62_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f912,f647,f809]) ).
fof(f914,plain,
( sQ61_spl
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f808,f276]) ).
fof(f915,plain,
( sQ61_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f914,f436,f439,f647,f806]) ).
fof(f948,plain,
( ~ sQ60_spl
| ~ l3_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f804,f230]) ).
fof(f949,plain,
( ~ sQ60_spl
| ~ sQ46_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f948,f436,f647,f803]) ).
fof(f1300,plain,
( ~ sQ50_spl
| k18_filter_2(sK0_skl,sK1_skl) = k2_filter_2(k1_lattice2(sK0_skl),sK1_skl)
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(paramodulation,[status(thm)],[f699,f382]) ).
fof(f1301,definition,
( sQ100_spl
<=> k18_filter_2(sK0_skl,sK1_skl) = k2_filter_2(k1_lattice2(sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1302,plain,
( ~ sQ100_spl
| k18_filter_2(sK0_skl,sK1_skl) = k2_filter_2(k1_lattice2(sK0_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f1301]) ).
fof(f1304,plain,
( ~ sQ50_spl
| sQ100_spl
| ~ sQ58_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1300,f436,f439,f647,f792,f1301,f698]) ).
fof(f1305,plain,
( ~ sQ100_spl
| k18_filter_2(sK0_skl,sK1_skl) = k2_filter_0(k1_lattice2(sK0_skl),sK1_skl)
| ~ m1_subset_1(sK1_skl,u1_struct_0(k1_lattice2(sK0_skl)))
| ~ l3_lattices(k1_lattice2(sK0_skl))
| ~ v10_lattices(k1_lattice2(sK0_skl))
| v3_struct_0(k1_lattice2(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f1302,f349]) ).
fof(f1307,definition,
( sQ101_spl
<=> k18_filter_2(sK0_skl,sK1_skl) = k2_filter_0(k1_lattice2(sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1308,plain,
( ~ sQ101_spl
| k18_filter_2(sK0_skl,sK1_skl) = k2_filter_0(k1_lattice2(sK0_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f1307]) ).
fof(f1310,plain,
( ~ sQ100_spl
| sQ101_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1305,f803,f806,f809,f795,f1307,f1301]) ).
fof(f2334,plain,
! [X0,X1,X2] :
( r1_tarski(k2_filter_0(X0,X2),k3_filter_0(X0,X1))
| ~ r2_hidden(X2,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(forward_subsumption_resolution,[status(thm)],[f373,f395]) ).
fof(f2428,definition,
( sQ204_spl
<=> k3_filter_2(k1_lattice2(sK0_skl),sK2_skl) = k19_filter_2(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2429,plain,
( ~ sQ204_spl
| k3_filter_2(k1_lattice2(sK0_skl),sK2_skl) = k19_filter_2(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f2428]) ).
fof(f2526,definition,
! [X0] :
( sQ215_spl
<=> ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| v1_xboole_0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2527,plain,
! [X0] :
( ~ sQ215_spl
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| v1_xboole_0(X0) ),
inference(component_clause,[status(thm)],[f2526]) ).
fof(f2536,plain,
! [X0] :
( ~ sQ68_spl
| k3_filter_2(k1_lattice2(sK0_skl),sK2_skl) = k19_filter_2(sK0_skl,sK2_skl)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK0_skl))))
| v1_xboole_0(sK2_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| v1_xboole_0(X0)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(paramodulation,[status(thm)],[f883,f388]) ).
fof(f2542,plain,
( ~ sQ68_spl
| sQ204_spl
| ~ sQ67_spl
| sQ14_spl
| sQ215_spl
| ~ sQ46_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f2536,f436,f439,f647,f2526,f476,f851,f2428,f882]) ).
fof(f2550,plain,
( ~ sQ215_spl
| v1_xboole_0(sK2_skl) ),
inference(resolution,[status(thm)],[f2527,f110]) ).
fof(f2570,plain,
( ~ sQ215_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f2550,f476,f2526]) ).
fof(f2596,plain,
( ~ sQ204_spl
| k19_filter_2(sK0_skl,sK2_skl) = k3_filter_0(k1_lattice2(sK0_skl),sK2_skl)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK0_skl))))
| v1_xboole_0(sK2_skl)
| ~ l3_lattices(k1_lattice2(sK0_skl))
| ~ v10_lattices(k1_lattice2(sK0_skl))
| v3_struct_0(k1_lattice2(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f2429,f351]) ).
fof(f2602,definition,
( sQ227_spl
<=> k19_filter_2(sK0_skl,sK2_skl) = k3_filter_0(k1_lattice2(sK0_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2603,plain,
( ~ sQ227_spl
| k19_filter_2(sK0_skl,sK2_skl) = k3_filter_0(k1_lattice2(sK0_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f2602]) ).
fof(f2605,plain,
( ~ sQ204_spl
| sQ227_spl
| ~ sQ67_spl
| sQ14_spl
| ~ sQ62_spl
| ~ sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f2596,f803,f806,f809,f476,f851,f2602,f2428]) ).
fof(f2612,plain,
! [X0] :
( ~ sQ227_spl
| r1_tarski(k2_filter_0(k1_lattice2(sK0_skl),X0),k19_filter_2(sK0_skl,sK2_skl))
| ~ r2_hidden(X0,sK2_skl)
| ~ m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK0_skl))))
| v1_xboole_0(sK2_skl)
| ~ l3_lattices(k1_lattice2(sK0_skl))
| ~ v10_lattices(k1_lattice2(sK0_skl))
| v3_struct_0(k1_lattice2(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f2603,f2334]) ).
fof(f2614,definition,
! [X0] :
( sQ229_spl
<=> ( r1_tarski(k2_filter_0(k1_lattice2(sK0_skl),X0),k19_filter_2(sK0_skl,sK2_skl))
| ~ r2_hidden(X0,sK2_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2615,plain,
! [X0] :
( ~ sQ229_spl
| r1_tarski(k2_filter_0(k1_lattice2(sK0_skl),X0),k19_filter_2(sK0_skl,sK2_skl))
| ~ r2_hidden(X0,sK2_skl) ),
inference(component_clause,[status(thm)],[f2614]) ).
fof(f2617,plain,
( ~ sQ227_spl
| sQ229_spl
| ~ sQ67_spl
| sQ14_spl
| ~ sQ62_spl
| ~ sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f2612,f803,f806,f809,f476,f851,f2614,f2602]) ).
fof(f2624,plain,
( ~ sQ101_spl
| ~ sQ229_spl
| r1_tarski(k18_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK2_skl))
| ~ r2_hidden(sK1_skl,sK2_skl) ),
inference(paramodulation,[status(thm)],[f1308,f2615]) ).
fof(f2629,definition,
( sQ232_spl
<=> r1_tarski(k18_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2630,plain,
( ~ sQ232_spl
| r1_tarski(k18_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f2629]) ).
fof(f2632,plain,
( ~ sQ101_spl
| ~ sQ229_spl
| sQ232_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2624,f479,f2629,f2614,f1307]) ).
fof(f2633,plain,
( ~ sQ232_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2630,f112]) ).
fof(f2634,plain,
~ sQ232_spl,
inference(contradiction_clause,[status(thm)],[f2633]) ).
fof(f2635,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f449,f482,f491,f682,f701,f707,f798,f800,f854,f856,f885,f913,f915,f949,f1304,f1310,f2542,f2570,f2605,f2617,f2632,f2634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT311+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n026.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 23:36:22 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.30/1.09 % Refutation found
% 0.30/1.09 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.30/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.30/1.15 % Elapsed time: 0.673889 seconds
% 0.30/1.15 % CPU time: 4.598796 seconds
% 0.30/1.15 % Total memory used: 138.696 MB
% 0.30/1.15 % Net memory used: 135.560 MB
%------------------------------------------------------------------------------