%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT300+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 01:56:42 PM UTC 2026
% Result : Theorem 2.75s 0.77s
% Output : Proof 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 169 ( 62 ~; 75 |; 22 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 64 ( 0 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(f14_nnf,plain,
! [A] :
( ! [B] :
( 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(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] :
( 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(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c27,plain,
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_lattice4(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f0,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_2) ).
fof(f0_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(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,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(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,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(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c1,plain,
v10_lattices(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p117,plain,
( m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sk0)))
| ~ m2_lattice4(X0,sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(c2,plain,
l3_lattices(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p258,plain,
( m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sk0)))
| ~ m2_lattice4(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p117,c2]) ).
fof(f13,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(f13_nnf,plain,
! [A] :
( ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
| ~ m2_filter_2(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c26,plain,
( m2_lattice4(X1,X0)
| ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p110,plain,
( m2_lattice4(X0,sk0)
| ~ m2_filter_2(X0,sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c26,c1]) ).
cnf(p221,plain,
( m2_lattice4(X0,sk0)
| ~ m2_filter_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p110,c2]) ).
cnf(c3,plain,
m2_filter_2(sk1,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p228,plain,
( m2_lattice4(sk1,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p221,c3]) ).
cnf(p261,plain,
( v3_struct_0(sk0)
| m1_subset_1(sk1,k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p258,p228]) ).
cnf(p263,plain,
( m1_subset_1(sk1,k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p261]) ).
fof(f39,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f39_nnf,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c59,plain,
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f37,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f37_nnf,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c56,plain,
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f21,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f21_nnf,plain,
! [A] :
? [B] : m1_subset_1(B,A),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A] : m1_subset_1(sk7(A),A),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f21_nnf]) ).
cnf(c34,plain,
m1_subset_1(sk7(X0),X0),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p133,plain,
( r2_hidden(sk7(X0),X0)
| v1_xboole_0(X0) ),
inference(resolution,[status(thm)],[c56,c34]) ).
cnf(p175,plain,
( v1_xboole_0(X0)
| m1_subset_1(sk7(X0),X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(resolution,[status(thm)],[c59,p133]) ).
cnf(p266,plain,
( v1_xboole_0(sk1)
| m1_subset_1(sk7(sk1),u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p263,p175]) ).
cnf(c4,plain,
( ~ r2_hidden(X2,sk1)
| ~ m1_subset_1(X2,u1_struct_0(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p274,plain,
( ~ r2_hidden(sk7(sk1),sk1)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p266,c4]) ).
cnf(p276,plain,
( v1_xboole_0(sk1)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p274,p133]) ).
cnf(p277,plain,
( v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p276]) ).
cnf(c25,plain,
( ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p107,plain,
( ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c25,c1]) ).
cnf(p185,plain,
( ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p107,c2]) ).
cnf(p186,plain,
( ~ v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p185,c3]) ).
cnf(p283,plain,
( v3_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p277,p186]) ).
cnf(p290,plain,
v3_struct_0(sk0),
inference(factoring,[status(thm)],[p283]) ).
cnf(c0,plain,
~ v3_struct_0(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p291,plain,
$false,
inference(resolution,[status(thm)],[p290,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT300+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 20:56:03 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.75/0.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/0.77 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------