%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT300+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 : n007.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 07:50:05 AM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 15 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 206 ( 84 ~; 81 |; 26 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 72 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_l1_lattices,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
fof(dt_l3_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_struct_0,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m1_struct_0(C,A,B)
=> m1_subset_1(C,u1_struct_0(A)) ) ),
file('theBenchmark.p',dt_m1_struct_0) ).
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(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(redefinition_m1_struct_0,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ! [C] :
( m1_struct_0(C,A,B)
<=> m1_subset_1(C,B) ) ),
file('theBenchmark.p',redefinition_m1_struct_0) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
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]) ).
cnf(c_51,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_52,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_53,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] :
( ~ 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,sK1)
| ~ m1_subset_1(C,u1_struct_0(sK0)) )
& m2_filter_2(sK1,sK0)
& l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_43]) ).
cnf(c_58,negated_conjecture,
v10_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_67,plain,
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(clausify,[status(thm)],[dt_l1_lattices]) ).
cnf(c_68,plain,
( l1_lattices(A)
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[dt_l3_lattices]) ).
cnf(c_70,plain,
( m1_subset_1(C,u1_struct_0(A))
| ~ m1_struct_0(C,A,B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m1_struct_0]) ).
cnf(c_72,plain,
( ~ l3_lattices(A)
| l1_struct_0(A) ),
inference(resolve,[status(thm)],[c_67,c_68]) ).
cnf(c_81,plain,
( ~ m1_subset_1(C,B)
| m1_struct_0(C,A,B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[redefinition_m1_struct_0]) ).
cnf(c_96,plain,
( ~ l3_lattices(A)
| ~ m1_subset_1(C,B)
| m1_struct_0(C,A,B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| v3_struct_0(A) ),
inference(resolve,[status(thm)],[c_81,c_72]) ).
cnf(c_122,plain,
( ~ l3_lattices(A)
| m1_subset_1(C,u1_struct_0(A))
| ~ m1_struct_0(C,A,B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| v3_struct_0(A) ),
inference(resolve,[status(thm)],[c_70,c_72]) ).
cnf(c_142,negated_conjecture,
( ~ v1_xboole_0(A)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_58,c_51]) ).
cnf(c_143,negated_conjecture,
( m2_lattice4(A,sK0)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_58,c_52]) ).
cnf(c_144,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_58,c_53]) ).
cnf(c_149,negated_conjecture,
( ~ r2_hidden(A,sK1)
| ~ m1_subset_1(A,u1_struct_0(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_150,negated_conjecture,
m2_filter_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_151,negated_conjecture,
l3_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_152,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_158,plain,
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
fof(nnf_21,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : m1_subset_1(sK2(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(B,sK2(A))],[nnf_21]) ).
cnf(c_169,plain,
m1_subset_1(sK2(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_594,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_152,c_144]) ).
cnf(c_187,negated_conjecture,
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m2_lattice4(A,sK0) ),
inference(resolve,[status(thm)],[c_151,c_594]) ).
cnf(c_595,negated_conjecture,
( m2_lattice4(A,sK0)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_152,c_143]) ).
cnf(c_188,negated_conjecture,
( m2_lattice4(A,sK0)
| ~ m2_filter_2(A,sK0) ),
inference(resolve,[status(thm)],[c_151,c_595]) ).
cnf(c_596,negated_conjecture,
( ~ v1_xboole_0(A)
| ~ m2_filter_2(A,sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_152,c_142]) ).
cnf(c_189,negated_conjecture,
( ~ v1_xboole_0(A)
| ~ m2_filter_2(A,sK0) ),
inference(resolve,[status(thm)],[c_151,c_596]) ).
cnf(c_272,plain,
( r2_hidden(sK2(A),A)
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_169,c_158]) ).
cnf(c_333,plain,
m2_lattice4(sK1,sK0),
inference(resolve,[status(thm)],[c_188,c_150]) ).
cnf(c_335,plain,
~ v1_xboole_0(sK1),
inference(resolve,[status(thm)],[c_189,c_150]) ).
cnf(c_381,plain,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_333,c_187]) ).
cnf(c_597,negated_conjecture,
( ~ m1_subset_1(sK2(sK1),u1_struct_0(sK0))
| v1_xboole_0(sK1) ),
inference(resolve,[status(thm)],[c_272,c_149]) ).
cnf(c_433,negated_conjecture,
~ m1_subset_1(sK2(sK1),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_335,c_597]) ).
cnf(c_598,plain,
( ~ l3_lattices(sK0)
| ~ m1_subset_1(A,sK1)
| m1_struct_0(A,sK0,sK1)
| v1_xboole_0(sK1)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_381,c_96]) ).
cnf(c_599,negated_conjecture,
( ~ l3_lattices(sK0)
| ~ m1_subset_1(A,sK1)
| m1_struct_0(A,sK0,sK1)
| v1_xboole_0(sK1) ),
inference(resolve,[status(thm)],[c_152,c_598]) ).
cnf(c_600,negated_conjecture,
( ~ l3_lattices(sK0)
| ~ m1_subset_1(A,sK1)
| m1_struct_0(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_335,c_599]) ).
cnf(c_585,negated_conjecture,
( ~ m1_subset_1(A,sK1)
| m1_struct_0(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_151,c_600]) ).
cnf(c_601,negated_conjecture,
( ~ l3_lattices(sK0)
| m1_subset_1(B,u1_struct_0(sK0))
| ~ m1_struct_0(B,sK0,A)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| v1_xboole_0(A) ),
inference(resolve,[status(thm)],[c_122,c_152]) ).
cnf(c_602,negated_conjecture,
( ~ l3_lattices(sK0)
| m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_struct_0(A,sK0,sK1)
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_601,c_335]) ).
cnf(c_603,negated_conjecture,
( ~ l3_lattices(sK0)
| m1_subset_1(A,u1_struct_0(sK0))
| ~ m1_struct_0(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_602,c_381]) ).
cnf(c_604,negated_conjecture,
( ~ l3_lattices(sK0)
| ~ m1_struct_0(sK2(sK1),sK0,sK1) ),
inference(resolve,[status(thm)],[c_603,c_433]) ).
cnf(c_589,negated_conjecture,
~ m1_struct_0(sK2(sK1),sK0,sK1),
inference(resolve,[status(thm)],[c_604,c_151]) ).
cnf(c_605,plain,
m1_struct_0(sK2(sK1),sK0,sK1),
inference(resolve,[status(thm)],[c_585,c_169]) ).
cnf(c_593,plain,
$false,
inference(resolve,[status(thm)],[c_589,c_605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT300+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 20:34:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1815893 was started by sandbox2 on n007,
% 0.10/0.37 % Fri Sep 25 20:34:53 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.43
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43
% 0.10/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.10/0.43 % Length of proof is 40.
% 0.10/0.43 % Level of proof is 7.
% 0.10/0.43 % Maximum clause weight is 34.000.
% 0.10/0.43 % Given clauses 179.
% 0.10/0.43
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------