%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT300+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:50:06 AM UTC 2026
% Result : Theorem 72.03s 11.28s
% Output : CNFRefutation 72.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 183 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 206 ( 77 ~; 75 |; 40 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('theBenchmark.p',fc1_lattice2) ).
fof(fc6_lattice2,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('theBenchmark.p',fc6_lattice2) ).
fof(t18_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( u1_lattices(A) = u2_lattices(k1_lattice2(A))
& u2_lattices(A) = u1_lattices(k1_lattice2(A))
& u1_struct_0(A) = u1_struct_0(k1_lattice2(A)) ) ),
file('theBenchmark.p',t18_lattice2) ).
fof(dt_k1_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) ) ),
file('theBenchmark.p',dt_k1_lattice2) ).
fof(redefinition_m1_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_2(B,A)
<=> m1_filter_0(B,A) ) ),
file('theBenchmark.p',redefinition_m1_filter_2) ).
fof(t11_filter_0,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(A)) ) ) ),
file('theBenchmark.p',t11_filter_0) ).
fof(t21_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
<=> m1_filter_2(B,k1_lattice2(A)) ) ),
file('theBenchmark.p',t21_filter_2) ).
fof(t24_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(A)) ) ) ),
file('theBenchmark.p',t24_filter_2) ).
fof(t24_filter_2_neg,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(A)) ) ) ),
inference(assume_negation,[status(cth)],[t24_filter_2]) ).
fof(nnf_271,plain,
! [A] :
( ! [B] :
( ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_filter_0(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t11_filter_0]) ).
fof(sk_t11_filter_0_sk,plain,
! [A] :
( ! [B] :
( ( r2_hidden(sK0(A,B),B)
& m1_subset_1(sK0(A,B),u1_struct_0(A)) )
| ~ m1_filter_0(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_271]) ).
fof(sk_t11_filter_0,plain,
( ! [VAR_0,VAR_1] :
( r2_hidden(sK0(VAR_0,VAR_1),VAR_1)
| ~ m1_filter_0(VAR_1,VAR_0)
| ~ l3_lattices(VAR_0)
| ~ v10_lattices(VAR_0)
| v3_struct_0(VAR_0) )
& ! [VAR_0,VAR_1] :
( m1_subset_1(sK0(VAR_0,VAR_1),u1_struct_0(VAR_0))
| ~ m1_filter_0(VAR_1,VAR_0)
| ~ l3_lattices(VAR_0)
| ~ v10_lattices(VAR_0)
| v3_struct_0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t11_filter_0_sk]) ).
cnf(c_902,plain,
( m1_subset_1(sK0(A,B),u1_struct_0(A))
| ~ m1_filter_0(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(split_conjunct,[status(thm)],[sk_t11_filter_0]) ).
cnf(c_903,plain,
( r2_hidden(sK0(A,B),B)
| ~ m1_filter_0(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(split_conjunct,[status(thm)],[sk_t11_filter_0]) ).
cnf(c_1183,plain,
( m1_filter_2(B,k1_lattice2(A))
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t21_filter_2]) ).
cnf(c_1319,plain,
( ~ v3_struct_0(k1_lattice2(A))
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_lattice2]) ).
cnf(c_1327,plain,
( v10_lattices(k1_lattice2(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc6_lattice2]) ).
cnf(c_1330,plain,
( u1_struct_0(k1_lattice2(A)) = u1_struct_0(A)
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t18_lattice2]) ).
cnf(c_1376,plain,
( l3_lattices(k1_lattice2(A))
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[dt_k1_lattice2]) ).
cnf(c_1396,plain,
( m1_filter_0(B,A)
| ~ m1_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[redefinition_m1_filter_2]) ).
fof(nnf_385,plain,
? [A] :
( ? [B] :
( ! [C] :
( ~ r2_hidden(C,B)
| ~ m1_subset_1(C,u1_struct_0(A)) )
& m2_filter_2(B,A) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t24_filter_2_neg]) ).
fof(sk_t24_filter_2_neg,plain,
( ! [C] :
( ~ r2_hidden(C,sK2)
| ~ m1_subset_1(C,u1_struct_0(sK1)) )
& m2_filter_2(sK2,sK1)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_385]) ).
cnf(c_1458,negated_conjecture,
~ v3_struct_0(sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1459,negated_conjecture,
v10_lattices(sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1460,negated_conjecture,
l3_lattices(sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1461,negated_conjecture,
m2_filter_2(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1462,negated_conjecture,
( ~ r2_hidden(A,sK2)
| ~ m1_subset_1(A,u1_struct_0(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_20588,negated_conjecture,
( m1_filter_2(sK2,k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1461,c_1183]) ).
cnf(c_20589,negated_conjecture,
( m1_filter_2(sK2,k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(resolve,[status(thm)],[c_1458,c_20588]) ).
cnf(c_20590,negated_conjecture,
( m1_filter_2(sK2,k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(resolve,[status(thm)],[c_1459,c_20589]) ).
cnf(c_1638,negated_conjecture,
m1_filter_2(sK2,k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1460,c_20590]) ).
cnf(c_20591,negated_conjecture,
( ~ v3_struct_0(k1_lattice2(sK1))
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1319,c_1460]) ).
cnf(c_14902,negated_conjecture,
~ v3_struct_0(k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1458,c_20591]) ).
cnf(c_20592,negated_conjecture,
( v10_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1327,c_1459]) ).
cnf(c_20593,negated_conjecture,
( v10_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(resolve,[status(thm)],[c_1458,c_20592]) ).
cnf(c_15093,negated_conjecture,
v10_lattices(k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1460,c_20593]) ).
cnf(c_20594,negated_conjecture,
( u1_struct_0(k1_lattice2(sK1)) = u1_struct_0(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1330,c_1460]) ).
cnf(c_15208,negated_conjecture,
u1_struct_0(k1_lattice2(sK1)) = u1_struct_0(sK1),
inference(resolve,[status(thm)],[c_1458,c_20594]) ).
cnf(c_17462,plain,
l3_lattices(k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1376,c_1460]) ).
cnf(c_20595,plain,
( m1_filter_0(sK2,k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_1396,c_1638]) ).
cnf(c_20596,plain,
( m1_filter_0(sK2,k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_14902,c_20595]) ).
cnf(c_20597,plain,
( m1_filter_0(sK2,k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_15093,c_20596]) ).
cnf(c_18857,plain,
m1_filter_0(sK2,k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_17462,c_20597]) ).
cnf(c_20598,plain,
( r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_18857,c_903]) ).
cnf(c_20599,plain,
( r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_14902,c_20598]) ).
cnf(c_20600,plain,
( r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2)
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_15093,c_20599]) ).
cnf(c_18918,plain,
r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2),
inference(resolve,[status(thm)],[c_17462,c_20600]) ).
cnf(c_20601,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(k1_lattice2(sK1)))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_18857,c_902]) ).
cnf(c_20602,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(paramod,[status(thm)],[c_15208,c_20601]) ).
cnf(c_20603,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_14902,c_20602]) ).
cnf(c_20604,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_15093,c_20603]) ).
cnf(c_18919,plain,
m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_17462,c_20604]) ).
cnf(c_20605,negated_conjecture,
~ m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_18918,c_1462]) ).
cnf(c_20587,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_18919,c_20605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT300+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 20:40:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2156105 was started by sandbox on n015,
% 0.13/0.36 % Fri Sep 25 20:40:52 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 72.03/11.28
% 72.03/11.28 % SInE (scan): 291 to sos (tol 1.5x), 98 to usable (tol 2.0x), 34292 zapped, of 34681 axioms (depth 3).
% 72.03/11.28
% 72.03/11.28 % From the command line: assign(max_seconds, 300).
% 72.03/11.28
% 72.03/11.28 % given #500 (W,wt=8): 2614 m1_subset_1(k1_zfmisc_1(f7(k1_zfmisc_1(A))),k1_zfmisc_1(k1_zfmisc_1(A))). [resolve(1839,a,429,b)].
% 72.03/11.28
% 72.03/11.28 % given #1000 (F,wt=11): 13948 -r2_hidden(k1_zfmisc_1(k1_zfmisc_1(k1_zfmisc_1(A))),k1_relat_1(k2_zfmisc_1(k1_zfmisc_1(k1_xboole_0),f105(c16)))). [resolve(13888,a,12666,b)].
% 72.03/11.28
% 72.03/11.28 % given #1500 (W,wt=8): 16592 v1_funct_1(f96(k1_numbers,f3(k5_numbers))) | v1_relat_1(f7(k5_numbers)). [resolve(16425,b,432,a)].
% 72.03/11.28
% 72.03/11.28 % given #2000 (F,wt=10): 19230 -r2_hidden(k1_zfmisc_1(u1_struct_0(c16)),k5_lattices(c15)) | -r2_hidden(f33(c15),c17). [resolve(19207,a,18812,b)].
% 72.03/11.28
% 72.03/11.28 % SZS status Theorem for theBenchmark
% 72.03/11.28
% 72.03/11.28 % Proof 1 at 9.33 (+ 0.90) seconds.
% 72.03/11.28 % Length of proof is 30.
% 72.03/11.28 % Level of proof is 5.
% 72.03/11.28 % Maximum clause weight is 112.000.
% 72.03/11.28 % Given clauses 2213.
% 72.03/11.28
% 72.03/11.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------