%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:50:09 AM UTC 2026
% Result : Theorem 13.21s 2.10s
% Output : CNFRefutation 13.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 81 ( 25 unt; 0 def)
% Number of atoms : 309 ( 17 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 378 ( 150 ~; 150 |; 56 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 1 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d11_filter_2,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] :
( m2_filter_2(C,A)
=> ( C = k19_filter_2(A,B)
<=> ( ! [D] :
( m2_filter_2(D,A)
=> ( r1_tarski(B,D)
=> r1_tarski(C,D) ) )
& r1_tarski(B,C) ) ) ) ) ),
file('theBenchmark.p',d11_filter_2) ).
fof(dt_k19_filter_2,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) )
=> m2_filter_2(k19_filter_2(A,B),A) ),
file('theBenchmark.p',dt_k19_filter_2) ).
fof(dt_m2_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) ) ) ),
file('theBenchmark.p',dt_m2_filter_2) ).
fof(dt_m2_lattice4,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_lattice4(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('theBenchmark.p',dt_m2_lattice4) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( r1_tarski(B,C)
& r1_tarski(A,B) )
=> r1_tarski(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t39_filter_2,conjecture,
! [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(A)))
& ~ v1_xboole_0(C) )
=> ! [D] :
( ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(D) )
=> ( r1_tarski(k19_filter_2(A,k19_filter_2(A,B)),k19_filter_2(A,B))
& ( r1_tarski(C,D)
=> r1_tarski(k19_filter_2(A,C),k19_filter_2(A,D)) ) ) ) ) ) ),
file('theBenchmark.p',t39_filter_2) ).
fof(t39_filter_2_neg,negated_conjecture,
~ ! [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(A)))
& ~ v1_xboole_0(C) )
=> ! [D] :
( ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(D) )
=> ( r1_tarski(k19_filter_2(A,k19_filter_2(A,B)),k19_filter_2(A,B))
& ( r1_tarski(C,D)
=> r1_tarski(k19_filter_2(A,C),k19_filter_2(A,D)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t39_filter_2]) ).
cnf(c_51,plain,
( r1_tarski(B,C)
| k19_filter_2(A,B) != C
| ~ m2_filter_2(C,A)
| ~ 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(clausify,[status(thm)],[d11_filter_2]) ).
cnf(c_52,plain,
( r1_tarski(C,D)
| ~ r1_tarski(B,D)
| ~ m2_filter_2(D,A)
| k19_filter_2(A,B) != C
| ~ m2_filter_2(C,A)
| ~ 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(clausify,[status(thm)],[d11_filter_2]) ).
cnf(c_56,plain,
( m2_filter_2(k19_filter_2(A,B),A)
| ~ 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(clausify,[status(thm)],[dt_k19_filter_2]) ).
cnf(c_57,plain,
( ~ v1_xboole_0(B)
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m2_filter_2]) ).
cnf(c_58,plain,
( m2_lattice4(B,A)
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m2_filter_2]) ).
cnf(c_59,plain,
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_lattice4(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m2_lattice4]) ).
fof(nnf_43,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ( ~ r1_tarski(k19_filter_2(A,k19_filter_2(A,B)),k19_filter_2(A,B))
| ( ~ r1_tarski(k19_filter_2(A,C),k19_filter_2(A,D))
& r1_tarski(C,D) ) )
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(D) )
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(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(fof_nnf,[status(thm)],[t39_filter_2_neg]) ).
fof(sk_t39_filter_2_neg_sk,plain,
( ( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ( ~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3))
& r1_tarski(sK2,sK3) ) )
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK3)
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK2)
& m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK1)
& l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_43]) ).
fof(sk_t39_filter_2_neg,plain,
( ( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)) )
& ( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| r1_tarski(sK2,sK3) )
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK3)
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK2)
& m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v1_xboole_0(sK1)
& l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t39_filter_2_neg_sk]) ).
cnf(c_64,negated_conjecture,
v10_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_113,plain,
r1_tarski(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_115,plain,
( r1_tarski(A,C)
| ~ r1_tarski(B,C)
| ~ r1_tarski(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
cnf(c_124,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_125,negated_conjecture,
l3_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_126,negated_conjecture,
~ v1_xboole_0(sK1),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_127,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_128,negated_conjecture,
~ v1_xboole_0(sK2),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_129,negated_conjecture,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_130,negated_conjecture,
~ v1_xboole_0(sK3),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_131,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_132,negated_conjecture,
( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| r1_tarski(sK2,sK3) ),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_133,negated_conjecture,
( ~ r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t39_filter_2_neg]) ).
cnf(c_142,negated_conjecture,
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_lattice4(A,sK0)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_64,c_59]) ).
cnf(c_4204,negated_conjecture,
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_lattice4(A,sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_124,c_142]) ).
cnf(c_143,negated_conjecture,
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_lattice4(A,sK0) ),
inference(resolve,[status(thm)],[c_125,c_4204]) ).
cnf(c_144,negated_conjecture,
( m2_lattice4(A,sK0)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_64,c_58]) ).
cnf(c_4205,negated_conjecture,
( m2_lattice4(A,sK0)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_124,c_144]) ).
cnf(c_145,negated_conjecture,
( m2_lattice4(A,sK0)
| ~ m2_filter_2(A,sK0) ),
inference(resolve,[status(thm)],[c_125,c_4205]) ).
cnf(c_146,negated_conjecture,
( ~ v1_xboole_0(A)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_64,c_57]) ).
cnf(c_4206,negated_conjecture,
( ~ v1_xboole_0(A)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_124,c_146]) ).
cnf(c_147,negated_conjecture,
( ~ v1_xboole_0(A)
| ~ m2_filter_2(A,sK0) ),
inference(resolve,[status(thm)],[c_125,c_4206]) ).
cnf(c_148,negated_conjecture,
( m2_filter_2(k19_filter_2(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_64,c_56]) ).
cnf(c_4207,negated_conjecture,
( m2_filter_2(k19_filter_2(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_124,c_148]) ).
cnf(c_149,negated_conjecture,
( m2_filter_2(k19_filter_2(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_125,c_4207]) ).
cnf(c_156,negated_conjecture,
( r1_tarski(B,C)
| ~ r1_tarski(A,C)
| ~ m2_filter_2(C,sK0)
| k19_filter_2(sK0,A) != B
| ~ m2_filter_2(B,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_64,c_52]) ).
cnf(c_4208,negated_conjecture,
( r1_tarski(B,C)
| ~ r1_tarski(A,C)
| ~ m2_filter_2(C,sK0)
| k19_filter_2(sK0,A) != B
| ~ m2_filter_2(B,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_124,c_156]) ).
cnf(c_157,negated_conjecture,
( r1_tarski(B,C)
| ~ r1_tarski(A,C)
| ~ m2_filter_2(C,sK0)
| k19_filter_2(sK0,A) != B
| ~ m2_filter_2(B,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_125,c_4208]) ).
cnf(c_158,negated_conjecture,
( r1_tarski(A,B)
| k19_filter_2(sK0,A) != B
| ~ m2_filter_2(B,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_64,c_51]) ).
cnf(c_4209,negated_conjecture,
( r1_tarski(A,B)
| k19_filter_2(sK0,A) != B
| ~ m2_filter_2(B,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_124,c_158]) ).
cnf(c_159,negated_conjecture,
( r1_tarski(A,B)
| k19_filter_2(sK0,A) != B
| ~ m2_filter_2(B,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_125,c_4209]) ).
cnf(c_4210,negated_conjecture,
( m2_filter_2(k19_filter_2(sK0,sK3),sK0)
| v1_xboole_0(sK3) ),
inference(resolve,[status(thm)],[c_149,c_131]) ).
cnf(c_238,negated_conjecture,
m2_filter_2(k19_filter_2(sK0,sK3),sK0),
inference(resolve,[status(thm)],[c_130,c_4210]) ).
cnf(c_4211,negated_conjecture,
( m2_filter_2(k19_filter_2(sK0,sK2),sK0)
| v1_xboole_0(sK2) ),
inference(resolve,[status(thm)],[c_149,c_129]) ).
cnf(c_239,negated_conjecture,
m2_filter_2(k19_filter_2(sK0,sK2),sK0),
inference(resolve,[status(thm)],[c_128,c_4211]) ).
cnf(c_4212,negated_conjecture,
( m2_filter_2(k19_filter_2(sK0,sK1),sK0)
| v1_xboole_0(sK1) ),
inference(resolve,[status(thm)],[c_149,c_127]) ).
cnf(c_240,negated_conjecture,
m2_filter_2(k19_filter_2(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_126,c_4212]) ).
cnf(c_4213,negated_conjecture,
( r1_tarski(sK3,A)
| k19_filter_2(sK0,sK3) != A
| ~ m2_filter_2(A,sK0)
| v1_xboole_0(sK3) ),
inference(resolve,[status(thm)],[c_159,c_131]) ).
cnf(c_4214,negated_conjecture,
( r1_tarski(sK3,k19_filter_2(sK0,sK3))
| k19_filter_2(sK0,sK3) != k19_filter_2(sK0,sK3)
| v1_xboole_0(sK3) ),
inference(resolve,[status(thm)],[c_4213,c_238]) ).
cnf(c_4215,plain,
( r1_tarski(sK3,k19_filter_2(sK0,sK3))
| v1_xboole_0(sK3) ),
inference(xxres,[status(thm)],[c_4214]) ).
cnf(c_354,negated_conjecture,
r1_tarski(sK3,k19_filter_2(sK0,sK3)),
inference(resolve,[status(thm)],[c_130,c_4215]) ).
cnf(c_4216,negated_conjecture,
( r1_tarski(k19_filter_2(sK0,sK2),B)
| ~ r1_tarski(A,B)
| ~ m2_filter_2(B,sK0)
| k19_filter_2(sK0,A) != k19_filter_2(sK0,sK2)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_239,c_157]) ).
cnf(c_357,negated_conjecture,
( r1_tarski(k19_filter_2(sK0,sK2),B)
| ~ r1_tarski(A,B)
| ~ m2_filter_2(B,sK0)
| k19_filter_2(sK0,sK2) != k19_filter_2(sK0,A)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A) ),
inference(copy,[status(thm)],[c_4216]) ).
cnf(c_365,plain,
( r1_tarski(B,k19_filter_2(sK0,sK1))
| ~ r1_tarski(A,k19_filter_2(sK0,sK1))
| k19_filter_2(sK0,A) != B
| ~ m2_filter_2(B,sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_240,c_157]) ).
cnf(c_370,plain,
~ v1_xboole_0(k19_filter_2(sK0,sK1)),
inference(resolve,[status(thm)],[c_240,c_147]) ).
cnf(c_371,plain,
m2_lattice4(k19_filter_2(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_240,c_145]) ).
cnf(c_415,plain,
( r1_tarski(A,k19_filter_2(sK0,sK3))
| ~ r1_tarski(A,sK3) ),
inference(resolve,[status(thm)],[c_354,c_115]) ).
cnf(c_425,plain,
m1_subset_1(k19_filter_2(sK0,sK1),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_371,c_143]) ).
cnf(c_4217,negated_conjecture,
( m2_filter_2(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),sK0)
| v1_xboole_0(k19_filter_2(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_425,c_149]) ).
cnf(c_1336,negated_conjecture,
m2_filter_2(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),sK0),
inference(resolve,[status(thm)],[c_370,c_4217]) ).
cnf(c_4218,plain,
( r1_tarski(A,k19_filter_2(sK0,sK1))
| ~ r1_tarski(k19_filter_2(sK0,sK1),k19_filter_2(sK0,sK1))
| k19_filter_2(sK0,k19_filter_2(sK0,sK1)) != A
| ~ m2_filter_2(A,sK0)
| v1_xboole_0(k19_filter_2(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_365,c_425]) ).
cnf(c_4219,plain,
( r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ r1_tarski(k19_filter_2(sK0,sK1),k19_filter_2(sK0,sK1))
| k19_filter_2(sK0,k19_filter_2(sK0,sK1)) != k19_filter_2(sK0,k19_filter_2(sK0,sK1))
| v1_xboole_0(k19_filter_2(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_4218,c_1336]) ).
cnf(c_4220,plain,
( r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| ~ r1_tarski(k19_filter_2(sK0,sK1),k19_filter_2(sK0,sK1))
| v1_xboole_0(k19_filter_2(sK0,sK1)) ),
inference(xxres,[status(thm)],[c_4219]) ).
cnf(c_4221,plain,
( r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1))
| v1_xboole_0(k19_filter_2(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_4220,c_113]) ).
cnf(c_4131,plain,
r1_tarski(k19_filter_2(sK0,k19_filter_2(sK0,sK1)),k19_filter_2(sK0,sK1)),
inference(resolve,[status(thm)],[c_370,c_4221]) ).
cnf(c_4134,negated_conjecture,
~ r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)),
inference(resolve,[status(thm)],[c_4131,c_133]) ).
cnf(c_4135,negated_conjecture,
r1_tarski(sK2,sK3),
inference(resolve,[status(thm)],[c_4131,c_132]) ).
cnf(c_4139,plain,
r1_tarski(sK2,k19_filter_2(sK0,sK3)),
inference(resolve,[status(thm)],[c_4135,c_415]) ).
cnf(c_4222,negated_conjecture,
( r1_tarski(k19_filter_2(sK0,sK2),A)
| ~ r1_tarski(sK2,A)
| ~ m2_filter_2(A,sK0)
| k19_filter_2(sK0,sK2) != k19_filter_2(sK0,sK2)
| v1_xboole_0(sK2) ),
inference(resolve,[status(thm)],[c_357,c_129]) ).
cnf(c_4223,plain,
( r1_tarski(k19_filter_2(sK0,sK2),A)
| ~ r1_tarski(sK2,A)
| ~ m2_filter_2(A,sK0)
| v1_xboole_0(sK2) ),
inference(xxres,[status(thm)],[c_4222]) ).
cnf(c_4224,plain,
( r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3))
| ~ r1_tarski(sK2,k19_filter_2(sK0,sK3))
| v1_xboole_0(sK2) ),
inference(resolve,[status(thm)],[c_4223,c_238]) ).
cnf(c_4225,plain,
( r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3))
| v1_xboole_0(sK2) ),
inference(resolve,[status(thm)],[c_4224,c_4139]) ).
cnf(c_4226,negated_conjecture,
r1_tarski(k19_filter_2(sK0,sK2),k19_filter_2(sK0,sK3)),
inference(resolve,[status(thm)],[c_128,c_4225]) ).
cnf(c_4203,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4134,c_4226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 20:48:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3250777 was started by sandbox2 on n016,
% 0.09/0.37 % Fri Sep 25 20:48:16 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 13.21/2.10
% 13.21/2.10 % given #500 (F,wt=21): 916 -r2_hidden(k1_zfmisc_1(u1_struct_0(c8)),f5(c8)). [ur(119,b,234,a,c,314,a)].
% 13.21/2.10
% 13.21/2.10 % given #1000 (T,wt=24): 2122 -r1_tarski(u1_struct_0(c8),A) | r1_tarski(f6(u1_struct_0(c8)),A). [resolve(2116,a,115,a)].
% 13.21/2.10
% 13.21/2.10 % SZS status Theorem for theBenchmark
% 13.21/2.10
% 13.21/2.10 % Proof 1 at 1.48 (+ 0.21) seconds.
% 13.21/2.10 % Length of proof is 54.
% 13.21/2.10 % Level of proof is 11.
% 13.21/2.10 % Maximum clause weight is 40.000.
% 13.21/2.10 % Given clauses 1383.
% 13.21/2.10
% 13.21/2.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------