%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT303+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 01:56:43 PM UTC 2026
% Result : Theorem 24.31s 3.55s
% Output : Proof 24.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 111 ( 13 unt; 0 def)
% Number of atoms : 436 ( 13 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 470 ( 145 ~; 229 |; 71 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 61 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_filter_2(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).
fof(f12_nnf,plain,
! [A] :
( ! [B] :
( k5_filter_2(A,B) = B
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B] :
( k5_filter_2(A,B) = B
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c29,plain,
( k5_filter_2(X0,X1) = X1
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f0,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(A),B),A)
=> v13_lattices(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_2) ).
fof(f0_neg,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( m2_filter_2(k6_domain_1(u1_struct_0(A),B),A)
=> v13_lattices(A) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A] :
( ? [B] :
( ~ v13_lattices(A)
& m2_filter_2(k6_domain_1(u1_struct_0(A),B),A)
& m1_subset_1(B,u1_struct_0(A)) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( ~ v13_lattices(sk0)
& m2_filter_2(k6_domain_1(u1_struct_0(sk0),sk1),sk0)
& m1_subset_1(sk1,u1_struct_0(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(p268,plain,
( k5_filter_2(sk0,X0) = X0
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c29,c1]) ).
cnf(c2,plain,
l3_lattices(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p271,plain,
( k5_filter_2(sk0,X0) = X0
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p268,c2]) ).
cnf(c3,plain,
m1_subset_1(sk1,u1_struct_0(sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p272,plain,
( k5_filter_2(sk0,sk1) = sk1
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p271,c3]) ).
fof(f19,axiom,
! [A,B] :
( ( m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k5_filter_2(A,B),u1_struct_0(k1_lattice2(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).
fof(f19_nnf,plain,
! [A,B] :
( m1_subset_1(k5_filter_2(A,B),u1_struct_0(k1_lattice2(A)))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B] :
( m1_subset_1(k5_filter_2(A,B),u1_struct_0(k1_lattice2(A)))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c38,plain,
( m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0)))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p325,plain,
( m1_subset_1(k5_filter_2(sk0,X0),u1_struct_0(k1_lattice2(sk0)))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c38,c1]) ).
cnf(p1218,plain,
( m1_subset_1(k5_filter_2(sk0,X0),u1_struct_0(k1_lattice2(sk0)))
| ~ m1_subset_1(X0,u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p325,c2]) ).
cnf(p1299,plain,
( m1_subset_1(k5_filter_2(sk0,sk1),u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1218,c3]) ).
cnf(p1301,plain,
( m1_subset_1(sk1,u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p272,p1299]) ).
cnf(p1304,plain,
( m1_subset_1(sk1,u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p1301]) ).
fof(f76,axiom,
! [A,B] :
( ( m1_subset_1(B,A)
& ~ v1_xboole_0(A) )
=> k6_domain_1(A,B) = k1_tarski(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
fof(f76_nnf,plain,
! [A,B] :
( k6_domain_1(A,B) = k1_tarski(B)
| ~ m1_subset_1(B,A)
| v1_xboole_0(A) ),
inference(nnf_transformation,[status(thm)],[f76]) ).
fof(f76_sk,plain,
! [A,B] :
( k6_domain_1(A,B) = k1_tarski(B)
| ~ m1_subset_1(B,A)
| v1_xboole_0(A) ),
inference(skolemisation,[status(esa)],[f76_nnf]) ).
cnf(c169,plain,
( k6_domain_1(X0,X1) = k1_tarski(X1)
| ~ m1_subset_1(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(esa)],[f76_sk]) ).
cnf(p1306,plain,
( k6_domain_1(u1_struct_0(k1_lattice2(sk0)),sk1) = k1_tarski(sk1)
| v1_xboole_0(u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1304,c169]) ).
fof(f80,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( m1_filter_0(k6_domain_1(u1_struct_0(A),B),A)
=> v14_lattices(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).
fof(f80_nnf,plain,
! [A] :
( ! [B] :
( v14_lattices(A)
| ~ m1_filter_0(k6_domain_1(u1_struct_0(A),B),A)
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f80]) ).
fof(f80_sk,plain,
! [A,B] :
( v14_lattices(A)
| ~ m1_filter_0(k6_domain_1(u1_struct_0(A),B),A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f80_nnf]) ).
cnf(c175,plain,
( v14_lattices(X0)
| ~ m1_filter_0(k6_domain_1(u1_struct_0(X0),X1),X0)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f80_sk]) ).
fof(f58,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('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).
fof(f58_nnf,plain,
! [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)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [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)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c113,plain,
( v10_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(p985,plain,
( v10_lattices(k1_lattice2(sk0))
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c113,c1]) ).
cnf(p988,plain,
( v10_lattices(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p985,c2]) ).
cnf(p1297,plain,
( v3_struct_0(sk0)
| v14_lattices(k1_lattice2(sk0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(k1_lattice2(sk0)),X0),k1_lattice2(sk0))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sk0)))
| ~ l3_lattices(k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(resolution,[status(thm)],[c175,p988]) ).
fof(f14,axiom,
! [A] :
( l3_lattices(A)
=> ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).
fof(f14_nnf,plain,
! [A] :
( ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) )
| ~ l3_lattices(A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] :
( ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) )
| ~ l3_lattices(A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c33,plain,
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p303,plain,
l3_lattices(k1_lattice2(sk0)),
inference(resolution,[status(thm)],[c33,c2]) ).
cnf(p2970,plain,
( v3_struct_0(sk0)
| v14_lattices(k1_lattice2(sk0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(k1_lattice2(sk0)),X0),k1_lattice2(sk0))
| ~ m1_subset_1(X0,u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(resolution,[status(thm)],[p1297,p303]) ).
cnf(p2973,plain,
( v3_struct_0(sk0)
| v3_struct_0(sk0)
| v14_lattices(k1_lattice2(sk0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(k1_lattice2(sk0)),sk1),k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(resolution,[status(thm)],[p2970,p1304]) ).
cnf(p2976,plain,
( v3_struct_0(sk0)
| v14_lattices(k1_lattice2(sk0))
| ~ m1_filter_0(k6_domain_1(u1_struct_0(k1_lattice2(sk0)),sk1),k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(factoring,[status(thm)],[p2973]) ).
cnf(p2978,plain,
( v3_struct_0(sk0)
| v14_lattices(k1_lattice2(sk0))
| ~ m1_filter_0(k1_tarski(sk1),k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p1306,p2976]) ).
cnf(p2984,plain,
( v14_lattices(k1_lattice2(sk0))
| ~ m1_filter_0(k1_tarski(sk1),k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2978]) ).
cnf(p1244,plain,
( k6_domain_1(u1_struct_0(sk0),sk1) = k1_tarski(sk1)
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(resolution,[status(thm)],[c169,c3]) ).
fof(f77,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_2(B,A)
<=> m1_filter_0(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).
fof(f77_nnf,plain,
! [A] :
( ! [B] :
( ( ~ m1_filter_0(B,A)
| m1_filter_2(B,A) )
& ( m1_filter_0(B,A)
| ~ m1_filter_2(B,A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f77]) ).
fof(f77_sk,plain,
! [A,B] :
( ( ( ~ m1_filter_0(B,A)
| m1_filter_2(B,A) )
& ( m1_filter_0(B,A)
| ~ m1_filter_2(B,A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f77_nnf]) ).
cnf(c170,plain,
( m1_filter_0(X1,X0)
| ~ m1_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f77_sk]) ).
cnf(p1271,plain,
( v3_struct_0(sk0)
| m1_filter_0(X0,k1_lattice2(sk0))
| ~ m1_filter_2(X0,k1_lattice2(sk0))
| ~ l3_lattices(k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(resolution,[status(thm)],[c170,p988]) ).
cnf(p1603,plain,
( v3_struct_0(sk0)
| m1_filter_0(X0,k1_lattice2(sk0))
| ~ m1_filter_2(X0,k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(resolution,[status(thm)],[p1271,p303]) ).
fof(f82,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('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).
fof(f82_nnf,plain,
! [A] :
( ! [B] :
( ( ~ m1_filter_2(B,k1_lattice2(A))
| m2_filter_2(B,A) )
& ( m1_filter_2(B,k1_lattice2(A))
| ~ m2_filter_2(B,A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f82]) ).
fof(f82_sk,plain,
! [A,B] :
( ( ( ~ m1_filter_2(B,k1_lattice2(A))
| m2_filter_2(B,A) )
& ( m1_filter_2(B,k1_lattice2(A))
| ~ m2_filter_2(B,A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f82_nnf]) ).
cnf(c177,plain,
( m1_filter_2(X1,k1_lattice2(X0))
| ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f82_sk]) ).
cnf(p1313,plain,
( m1_filter_2(X0,k1_lattice2(sk0))
| ~ m2_filter_2(X0,sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c177,c1]) ).
cnf(p1318,plain,
( m1_filter_2(X0,k1_lattice2(sk0))
| ~ m2_filter_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1313,c2]) ).
cnf(c4,plain,
m2_filter_2(k6_domain_1(u1_struct_0(sk0),sk1),sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p1319,plain,
( m1_filter_2(k6_domain_1(u1_struct_0(sk0),sk1),k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1318,c4]) ).
cnf(p1605,plain,
( v3_struct_0(sk0)
| v3_struct_0(sk0)
| m1_filter_0(k6_domain_1(u1_struct_0(sk0),sk1),k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(resolution,[status(thm)],[p1603,p1319]) ).
cnf(p1609,plain,
( v3_struct_0(sk0)
| m1_filter_0(k6_domain_1(u1_struct_0(sk0),sk1),k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(factoring,[status(thm)],[p1605]) ).
cnf(p1610,plain,
( v3_struct_0(sk0)
| m1_filter_0(k1_tarski(sk1),k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(superposition,[status(thm)],[p1244,p1609]) ).
cnf(p2985,plain,
( v3_struct_0(sk0)
| v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(sk0))
| v14_lattices(k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p2984,p1610]) ).
cnf(p2990,plain,
( v3_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v14_lattices(k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2985]) ).
cnf(p2991,plain,
( v1_xboole_0(u1_struct_0(sk0))
| v14_lattices(k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2990]) ).
fof(f47,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f47_nnf,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c75,plain,
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
fof(f24,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f24_nnf,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c43,plain,
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p321,plain,
l1_lattices(k1_lattice2(sk0)),
inference(resolution,[status(thm)],[p303,c43]) ).
fof(f21,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(f21_nnf,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c40,plain,
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p324,plain,
l1_struct_0(k1_lattice2(sk0)),
inference(resolution,[status(thm)],[p321,c40]) ).
cnf(p669,plain,
( ~ v1_xboole_0(u1_struct_0(k1_lattice2(sk0)))
| v3_struct_0(k1_lattice2(sk0)) ),
inference(resolution,[status(thm)],[c75,p324]) ).
cnf(p2994,plain,
( v3_struct_0(k1_lattice2(sk0))
| v1_xboole_0(u1_struct_0(sk0))
| v14_lattices(k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p2991,p669]) ).
cnf(p2997,plain,
( v1_xboole_0(u1_struct_0(sk0))
| v14_lattices(k1_lattice2(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2994]) ).
fof(f87,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v13_lattices(A)
<=> v14_lattices(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).
fof(f87_nnf,plain,
! [A] :
( ( ( ~ v14_lattices(k1_lattice2(A))
| v13_lattices(A) )
& ( v14_lattices(k1_lattice2(A))
| ~ v13_lattices(A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f87]) ).
fof(f87_sk,plain,
! [A] :
( ( ( ~ v14_lattices(k1_lattice2(A))
| v13_lattices(A) )
& ( v14_lattices(k1_lattice2(A))
| ~ v13_lattices(A) ) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f87_nnf]) ).
cnf(c185,plain,
( ~ v14_lattices(k1_lattice2(X0))
| v13_lattices(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(p1395,plain,
( ~ v14_lattices(k1_lattice2(sk0))
| v13_lattices(sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c185,c1]) ).
cnf(p1399,plain,
( ~ v14_lattices(k1_lattice2(sk0))
| v13_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1395,c2]) ).
cnf(p2998,plain,
( v13_lattices(sk0)
| v3_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p2997,p1399]) ).
cnf(p2999,plain,
( v13_lattices(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2998]) ).
cnf(p261,plain,
l1_lattices(sk0),
inference(resolution,[status(thm)],[c43,c2]) ).
cnf(p267,plain,
l1_struct_0(sk0),
inference(resolution,[status(thm)],[p261,c40]) ).
cnf(p663,plain,
( ~ v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c75,p267]) ).
cnf(p3002,plain,
( v3_struct_0(sk0)
| v13_lattices(sk0)
| v3_struct_0(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p2999,p663]) ).
cnf(p3005,plain,
( v13_lattices(sk0)
| v3_struct_0(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p3002]) ).
fof(f46,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).
fof(f46_nnf,plain,
! [A] :
( ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [A] :
( ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c73,plain,
( ~ v3_struct_0(k1_lattice2(X0))
| ~ l3_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p641,plain,
( ~ v3_struct_0(k1_lattice2(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c73,c2]) ).
cnf(p3006,plain,
( v3_struct_0(sk0)
| v13_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p3005,p641]) ).
cnf(p3007,plain,
( v13_lattices(sk0)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p3006]) ).
cnf(c5,plain,
~ v13_lattices(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p3008,plain,
v3_struct_0(sk0),
inference(resolution,[status(thm)],[p3007,c5]) ).
cnf(c0,plain,
~ v3_struct_0(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p3010,plain,
$false,
inference(resolution,[status(thm)],[p3008,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT303+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 20:56:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.31/3.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.31/3.55 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------