%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT292+2 : 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 : n012.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 07:50:03 AM UTC 2026
% Result : Theorem 180.81s 41.49s
% Output : CNFRefutation 180.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 194 ( 8 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 236 ( 92 ~; 94 |; 44 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k11_lopclset,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( l1_pre_topc(k11_lopclset(A))
& v2_pre_topc(k11_lopclset(A))
& v1_pre_topc(k11_lopclset(A)) ) ),
file('theBenchmark.p',dt_k11_lopclset) ).
fof(fc4_lopclset,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v2_pre_topc(k11_lopclset(A))
& v1_pre_topc(k11_lopclset(A))
& ~ v3_struct_0(k11_lopclset(A)) ) ),
file('theBenchmark.p',fc4_lopclset) ).
fof(d9_lopclset,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k12_lopclset(A) = k6_lopclset(k11_lopclset(A)) ),
file('theBenchmark.p',d9_lopclset) ).
fof(t43_lopclset,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> r1_filter_1(A,k12_lopclset(A)) ),
file('theBenchmark.p',t43_lopclset) ).
fof(t44_lopclset,conjecture,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( r1_filter_1(A,k6_lopclset(B))
& l1_pre_topc(B)
& v2_pre_topc(B)
& ~ v3_struct_0(B) ) ),
file('theBenchmark.p',t44_lopclset) ).
fof(t44_lopclset_neg,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ? [B] :
( r1_filter_1(A,k6_lopclset(B))
& l1_pre_topc(B)
& v2_pre_topc(B)
& ~ v3_struct_0(B) ) ),
inference(assume_negation,[status(cth)],[t44_lopclset]) ).
cnf(c_4085,plain,
( v2_pre_topc(k11_lopclset(A))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k11_lopclset]) ).
cnf(c_4086,plain,
( l1_pre_topc(k11_lopclset(A))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k11_lopclset]) ).
cnf(c_4120,plain,
( ~ v3_struct_0(k11_lopclset(A))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc4_lopclset]) ).
cnf(c_4121,plain,
( k12_lopclset(A) = k6_lopclset(k11_lopclset(A))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[d9_lopclset]) ).
cnf(c_4122,plain,
( k6_lopclset(k11_lopclset(A)) = k12_lopclset(A)
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(copy,[status(thm)],[c_4121]) ).
cnf(c_4129,plain,
( r1_filter_1(A,k12_lopclset(A))
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t43_lopclset]) ).
fof(nnf_1329,plain,
? [A] :
( ! [B] :
( ~ r1_filter_1(A,k6_lopclset(B))
| ~ l1_pre_topc(B)
| ~ v2_pre_topc(B)
| v3_struct_0(B) )
& l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t44_lopclset_neg]) ).
fof(sk_t44_lopclset_neg,plain,
( ! [B] :
( ~ r1_filter_1(sK0,k6_lopclset(B))
| ~ l1_pre_topc(B)
| ~ v2_pre_topc(B)
| v3_struct_0(B) )
& l3_lattices(sK0)
& ~ v3_realset2(sK0)
& v17_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_1329]) ).
cnf(c_4130,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_lopclset_neg]) ).
cnf(c_4131,negated_conjecture,
v10_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_lopclset_neg]) ).
cnf(c_4132,negated_conjecture,
v17_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_lopclset_neg]) ).
cnf(c_4133,negated_conjecture,
~ v3_realset2(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_lopclset_neg]) ).
cnf(c_4134,negated_conjecture,
l3_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t44_lopclset_neg]) ).
cnf(c_4135,negated_conjecture,
( ~ r1_filter_1(sK0,k6_lopclset(A))
| ~ l1_pre_topc(A)
| ~ v2_pre_topc(A)
| v3_struct_0(A) ),
inference(split_conjunct,[status(thm)],[sk_t44_lopclset_neg]) ).
cnf(c_34990,negated_conjecture,
( v2_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_4085,c_4131]) ).
cnf(c_34991,negated_conjecture,
( v2_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4130,c_34990]) ).
cnf(c_34992,negated_conjecture,
( v2_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_4132,c_34991]) ).
cnf(c_34993,negated_conjecture,
( v2_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4133,c_34992]) ).
cnf(c_34112,negated_conjecture,
v2_pre_topc(k11_lopclset(sK0)),
inference(resolve,[status(thm)],[c_4134,c_34993]) ).
cnf(c_34994,negated_conjecture,
( l1_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_4086,c_4131]) ).
cnf(c_34995,negated_conjecture,
( l1_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4130,c_34994]) ).
cnf(c_34996,negated_conjecture,
( l1_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_4132,c_34995]) ).
cnf(c_34997,negated_conjecture,
( l1_pre_topc(k11_lopclset(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4133,c_34996]) ).
cnf(c_34123,negated_conjecture,
l1_pre_topc(k11_lopclset(sK0)),
inference(resolve,[status(thm)],[c_4134,c_34997]) ).
cnf(c_34998,negated_conjecture,
( ~ v3_struct_0(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_4120,c_4131]) ).
cnf(c_34999,negated_conjecture,
( ~ v3_struct_0(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4130,c_34998]) ).
cnf(c_35000,negated_conjecture,
( ~ v3_struct_0(k11_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_4132,c_34999]) ).
cnf(c_35001,negated_conjecture,
( ~ v3_struct_0(k11_lopclset(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4133,c_35000]) ).
cnf(c_34802,negated_conjecture,
~ v3_struct_0(k11_lopclset(sK0)),
inference(resolve,[status(thm)],[c_4134,c_35001]) ).
cnf(c_35002,negated_conjecture,
( k6_lopclset(k11_lopclset(sK0)) = k12_lopclset(sK0)
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_4122,c_4131]) ).
cnf(c_35003,negated_conjecture,
( k6_lopclset(k11_lopclset(sK0)) = k12_lopclset(sK0)
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4130,c_35002]) ).
cnf(c_35004,negated_conjecture,
( k6_lopclset(k11_lopclset(sK0)) = k12_lopclset(sK0)
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_4132,c_35003]) ).
cnf(c_35005,negated_conjecture,
( k6_lopclset(k11_lopclset(sK0)) = k12_lopclset(sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4133,c_35004]) ).
cnf(c_34911,negated_conjecture,
k6_lopclset(k11_lopclset(sK0)) = k12_lopclset(sK0),
inference(resolve,[status(thm)],[c_4134,c_35005]) ).
cnf(c_35006,negated_conjecture,
( r1_filter_1(sK0,k12_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_4129,c_4131]) ).
cnf(c_35007,negated_conjecture,
( r1_filter_1(sK0,k12_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4130,c_35006]) ).
cnf(c_35008,negated_conjecture,
( r1_filter_1(sK0,k12_lopclset(sK0))
| ~ l3_lattices(sK0)
| v3_realset2(sK0) ),
inference(resolve,[status(thm)],[c_4132,c_35007]) ).
cnf(c_35009,negated_conjecture,
( r1_filter_1(sK0,k12_lopclset(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_4133,c_35008]) ).
cnf(c_34978,negated_conjecture,
r1_filter_1(sK0,k12_lopclset(sK0)),
inference(resolve,[status(thm)],[c_4134,c_35009]) ).
cnf(c_35010,negated_conjecture,
( ~ r1_filter_1(sK0,k6_lopclset(k11_lopclset(sK0)))
| ~ l1_pre_topc(k11_lopclset(sK0))
| v3_struct_0(k11_lopclset(sK0)) ),
inference(resolve,[status(thm)],[c_4135,c_34112]) ).
cnf(c_35011,negated_conjecture,
( ~ r1_filter_1(sK0,k12_lopclset(sK0))
| ~ l1_pre_topc(k11_lopclset(sK0))
| v3_struct_0(k11_lopclset(sK0)) ),
inference(paramod,[status(thm)],[c_34911,c_35010]) ).
cnf(c_35012,negated_conjecture,
( ~ r1_filter_1(sK0,k12_lopclset(sK0))
| ~ l1_pre_topc(k11_lopclset(sK0)) ),
inference(resolve,[status(thm)],[c_34802,c_35011]) ).
cnf(c_35013,negated_conjecture,
~ r1_filter_1(sK0,k12_lopclset(sK0)),
inference(resolve,[status(thm)],[c_34123,c_35012]) ).
cnf(c_34989,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_34978,c_35013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT292+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/15.32 % Computer : n012.cluster.edu
% 0.05/15.32 % Model : x86_64 x86_64
% 0.05/15.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/15.32 % Memory : 8046.5625MB
% 0.05/15.32 % OS : Linux 6.8.0-71-generic
% 0.05/15.32 % CPULimit : 300
% 0.05/15.32 % WCLimit : 300
% 0.05/15.32 % DateTime : Fri Sep 25 20:31:20 UTC 2026
% 0.05/15.33 % CPUTime :
% 0.05/15.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/15.33 % Process 2927644 was started by sandbox on n012,
% 0.05/15.33 % Fri Sep 25 20:31:20 2026
% 0.05/15.33 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 180.81/41.49
% 180.81/41.49 % SInE (scan): 1030 to sos (tol 1.5x), 304 to usable (tol 2.0x), 5133 zapped, of 6467 axioms (depth 3).
% 180.81/41.49
% 180.81/41.49 % From the command line: assign(max_seconds, 300).
% 180.81/41.49
% 180.81/41.49 % given #500 (F,wt=19): 18690 -r1_tarski(c11,k2_relat_1(k1_xboole_0)) | -r2_hidden(k4_tarski(A,B),c11). [resolve(16927,a,1694,a)].
% 180.81/41.49
% 180.81/41.49 % given #1000 (W,wt=13): 27391 v1_xboole_0(A) | v1_xboole_0(B) | -v1_funct_2(c10,A,B). [back_unit_del(26444),unit_del(c,27370)].
% 180.81/41.49
% 180.81/41.49 % given #1500 (F,wt=19): 32154 -v1_membered(A) | -r1_tarski(A,c10) | -r2_hidden(f9(k5_numbers),A). [resolve(30569,a,27198,c)].
% 180.81/41.49
% 180.81/41.49 % SZS status Theorem for theBenchmark
% 180.81/41.49
% 180.81/41.49 % Proof 1 at 24.36 (+ 1.33) seconds.
% 180.81/41.49 % Length of proof is 23.
% 180.81/41.49 % Level of proof is 4.
% 180.81/41.49 % Maximum clause weight is 123.000.
% 180.81/41.49 % Given clauses 1835.
% 180.81/41.49
% 180.81/41.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------