%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT313+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 : n013.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 01:56:46 PM UTC 2026
% Result : Theorem 5.58s 11.32s
% Output : Proof 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 110 ( 9 unt; 0 def)
% Number of atoms : 444 ( 39 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 488 ( 154 ~; 266 |; 47 &)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 1 sgn 58 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) )
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( k19_filter_2(A,B) = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_2) ).
fof(f44_nnf,plain,
! [A] :
( ! [B] :
( ( k19_filter_2(A,B) = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) )
| ~ r2_hidden(k6_lattices(A),B)
| ~ v14_lattices(A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [A,B] :
( ( k19_filter_2(A,B) = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) )
| ~ r2_hidden(k6_lattices(A),B)
| ~ v14_lattices(A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c67,plain,
( k19_filter_2(X0,X1) = u1_struct_0(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
fof(f0,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( B = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_filter_2) ).
fof(f0_neg,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( B = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A] :
( ? [B] :
( ( B != u1_struct_0(A)
| ~ r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) )
& r2_hidden(k6_lattices(A),B)
& v14_lattices(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,
( ( sk1 != u1_struct_0(sk0)
| ~ r1_filter_2(u1_struct_0(sk0),sk1,k17_filter_2(sk0)) )
& r2_hidden(k6_lattices(sk0),sk1)
& v14_lattices(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(p271,plain,
( k19_filter_2(sk0,X0) = u1_struct_0(sk0)
| ~ r2_hidden(k6_lattices(sk0),X0)
| ~ v14_lattices(sk0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sk0)))
| v1_xboole_0(X0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c67,c1]) ).
cnf(c2,plain,
l3_lattices(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p1041,plain,
( k19_filter_2(sk0,X0) = u1_struct_0(sk0)
| ~ r2_hidden(k6_lattices(sk0),X0)
| ~ v14_lattices(sk0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sk0)))
| v1_xboole_0(X0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p271,c2]) ).
fof(f17,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/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).
fof(f17_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)],[f17]) ).
fof(f17_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)],[f17_nnf]) ).
cnf(c32,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)],[f17_sk]) ).
cnf(p131,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)],[c32,c1]) ).
cnf(p151,plain,
( m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sk0)))
| ~ m2_lattice4(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p131,c2]) ).
fof(f16,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/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).
fof(f16_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)],[f16]) ).
fof(f16_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)],[f16_nnf]) ).
cnf(c31,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)],[f16_sk]) ).
cnf(p128,plain,
( m2_lattice4(X0,sk0)
| ~ m2_filter_2(X0,sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c31,c1]) ).
cnf(p130,plain,
( m2_lattice4(X0,sk0)
| ~ m2_filter_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p128,c2]) ).
cnf(c3,plain,
m2_filter_2(sk1,sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p132,plain,
( m2_lattice4(sk1,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p130,c3]) ).
cnf(p152,plain,
( v3_struct_0(sk0)
| m1_subset_1(sk1,k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p151,p132]) ).
cnf(p160,plain,
( m1_subset_1(sk1,k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p152]) ).
cnf(p1875,plain,
( v3_struct_0(sk0)
| k19_filter_2(sk0,sk1) = u1_struct_0(sk0)
| ~ r2_hidden(k6_lattices(sk0),sk1)
| ~ v14_lattices(sk0)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1041,p160]) ).
cnf(p1894,plain,
( k19_filter_2(sk0,sk1) = u1_struct_0(sk0)
| ~ r2_hidden(k6_lattices(sk0),sk1)
| ~ v14_lattices(sk0)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p1875]) ).
cnf(c4,plain,
v14_lattices(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p1895,plain,
( k19_filter_2(sk0,sk1) = u1_struct_0(sk0)
| ~ r2_hidden(k6_lattices(sk0),sk1)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1894,c4]) ).
cnf(c5,plain,
r2_hidden(k6_lattices(sk0),sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p1896,plain,
( k19_filter_2(sk0,sk1) = u1_struct_0(sk0)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1895,c5]) ).
fof(f42,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_2) ).
fof(f42_nnf,plain,
! [A] :
( ! [B] :
( r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B)
| ~ m2_filter_2(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [A,B] :
( r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B)
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c63,plain,
( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1)
| ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p254,plain,
( r1_filter_2(u1_struct_0(sk0),k19_filter_2(sk0,X0),X0)
| ~ m2_filter_2(X0,sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c63,c1]) ).
cnf(p318,plain,
( r1_filter_2(u1_struct_0(sk0),k19_filter_2(sk0,X0),X0)
| ~ m2_filter_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p254,c2]) ).
cnf(p319,plain,
( r1_filter_2(u1_struct_0(sk0),k19_filter_2(sk0,sk1),sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p318,c3]) ).
cnf(p1898,plain,
( r1_filter_2(u1_struct_0(sk0),u1_struct_0(sk0),sk1)
| v3_struct_0(sk0)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p1896,p319]) ).
cnf(p1919,plain,
( r1_filter_2(u1_struct_0(sk0),u1_struct_0(sk0),sk1)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p1898]) ).
fof(f39,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> ( r1_filter_2(A,B,C)
=> r1_filter_2(A,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
fof(f39_nnf,plain,
! [A,B,C] :
( r1_filter_2(A,C,B)
| ~ r1_filter_2(A,B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C] :
( r1_filter_2(A,C,B)
| ~ r1_filter_2(A,B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c60,plain,
( r1_filter_2(X0,X2,X1)
| ~ r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f5,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k17_filter_2(A) = u1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_2) ).
fof(f5_nnf,plain,
! [A] :
( k17_filter_2(A) = u1_struct_0(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( k17_filter_2(A) = u1_struct_0(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c18,plain,
( k17_filter_2(X0) = u1_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p105,plain,
( k17_filter_2(sk0) = u1_struct_0(sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c18,c1]) ).
cnf(p106,plain,
( k17_filter_2(sk0) = u1_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p105,c2]) ).
fof(f6,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m2_filter_2(k17_filter_2(A),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_filter_2) ).
fof(f6_nnf,plain,
! [A] :
( m2_filter_2(k17_filter_2(A),A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] :
( m2_filter_2(k17_filter_2(A),A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c19,plain,
( m2_filter_2(k17_filter_2(X0),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p108,plain,
( m2_filter_2(k17_filter_2(sk0),sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c19,c1]) ).
cnf(p109,plain,
( m2_filter_2(k17_filter_2(sk0),sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p108,c2]) ).
cnf(p110,plain,
( m2_filter_2(u1_struct_0(sk0),sk0)
| v3_struct_0(sk0)
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p106,p109]) ).
cnf(p111,plain,
( m2_filter_2(u1_struct_0(sk0),sk0)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p110]) ).
cnf(p134,plain,
( v3_struct_0(sk0)
| m2_lattice4(u1_struct_0(sk0),sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p130,p111]) ).
cnf(p138,plain,
( m2_lattice4(u1_struct_0(sk0),sk0)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p134]) ).
cnf(p154,plain,
( v3_struct_0(sk0)
| m1_subset_1(u1_struct_0(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p151,p138]) ).
cnf(p167,plain,
( m1_subset_1(u1_struct_0(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p154]) ).
cnf(p228,plain,
( v3_struct_0(sk0)
| r1_filter_2(u1_struct_0(sk0),X0,u1_struct_0(sk0))
| ~ r1_filter_2(u1_struct_0(sk0),u1_struct_0(sk0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sk0)))
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(resolution,[status(thm)],[c60,p167]) ).
cnf(p880,plain,
( v3_struct_0(sk0)
| v3_struct_0(sk0)
| r1_filter_2(u1_struct_0(sk0),sk1,u1_struct_0(sk0))
| ~ r1_filter_2(u1_struct_0(sk0),u1_struct_0(sk0),sk1)
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(resolution,[status(thm)],[p228,p160]) ).
cnf(p1508,plain,
( v3_struct_0(sk0)
| r1_filter_2(u1_struct_0(sk0),sk1,u1_struct_0(sk0))
| ~ r1_filter_2(u1_struct_0(sk0),u1_struct_0(sk0),sk1)
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(factoring,[status(thm)],[p880]) ).
cnf(p1922,plain,
( v3_struct_0(sk0)
| r1_filter_2(u1_struct_0(sk0),sk1,u1_struct_0(sk0))
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1919,p1508]) ).
cnf(p2504,plain,
( r1_filter_2(u1_struct_0(sk0),sk1,u1_struct_0(sk0))
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p1922]) ).
cnf(c6,plain,
( sk1 != u1_struct_0(sk0)
| ~ r1_filter_2(u1_struct_0(sk0),sk1,k17_filter_2(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p107,plain,
( sk1 != u1_struct_0(sk0)
| ~ r1_filter_2(u1_struct_0(sk0),sk1,u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p106,c6]) ).
cnf(p2505,plain,
( sk1 != u1_struct_0(sk0)
| v3_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p2504,p107]) ).
cnf(p2507,plain,
( sk1 != u1_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2505]) ).
fof(f36,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> ( r1_filter_2(A,B,C)
<=> B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
fof(f36_nnf,plain,
! [A,B,C] :
( ( ( B != C
| r1_filter_2(A,B,C) )
& ( B = C
| ~ r1_filter_2(A,B,C) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [A,B,C] :
( ( ( B != C
| r1_filter_2(A,B,C) )
& ( B = C
| ~ r1_filter_2(A,B,C) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c56,plain,
( X1 = X2
| ~ r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p133,plain,
( v3_struct_0(sk0)
| m2_lattice4(k17_filter_2(sk0),sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p130,p109]) ).
cnf(p136,plain,
( m2_lattice4(k17_filter_2(sk0),sk0)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p133]) ).
cnf(p153,plain,
( v3_struct_0(sk0)
| m1_subset_1(k17_filter_2(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p151,p136]) ).
cnf(p164,plain,
( m1_subset_1(k17_filter_2(sk0),k1_zfmisc_1(u1_struct_0(sk0)))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p153]) ).
cnf(p193,plain,
( v3_struct_0(sk0)
| k17_filter_2(sk0) = X0
| ~ r1_filter_2(u1_struct_0(sk0),k17_filter_2(sk0),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sk0)))
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(resolution,[status(thm)],[c56,p164]) ).
cnf(p522,plain,
( v3_struct_0(sk0)
| v3_struct_0(sk0)
| k17_filter_2(sk0) = sk1
| ~ r1_filter_2(u1_struct_0(sk0),k17_filter_2(sk0),sk1)
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(resolution,[status(thm)],[p193,p160]) ).
cnf(p540,plain,
( v3_struct_0(sk0)
| k17_filter_2(sk0) = sk1
| ~ r1_filter_2(u1_struct_0(sk0),k17_filter_2(sk0),sk1)
| v1_xboole_0(u1_struct_0(sk0)) ),
inference(factoring,[status(thm)],[p522]) ).
cnf(p541,plain,
( v3_struct_0(sk0)
| k17_filter_2(sk0) = sk1
| ~ r1_filter_2(u1_struct_0(sk0),u1_struct_0(sk0),sk1)
| v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p106,p540]) ).
cnf(p560,plain,
( k17_filter_2(sk0) = sk1
| ~ r1_filter_2(u1_struct_0(sk0),u1_struct_0(sk0),sk1)
| v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p541]) ).
cnf(p1920,plain,
( k17_filter_2(sk0) = sk1
| v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(sk0)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p1919,p560]) ).
cnf(p1924,plain,
( k17_filter_2(sk0) = sk1
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p1920]) ).
cnf(p1926,plain,
( sk1 = u1_struct_0(sk0)
| v3_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(superposition,[status(thm)],[p1924,p106]) ).
cnf(p2417,plain,
( sk1 = u1_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p1926]) ).
cnf(p2509,plain,
( v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p2507,p2417]) ).
cnf(p2539,plain,
( v1_xboole_0(sk1)
| v3_struct_0(sk0)
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2509]) ).
cnf(p2540,plain,
( v1_xboole_0(sk1)
| v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2539]) ).
cnf(p2542,plain,
( v1_xboole_0(u1_struct_0(sk0))
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2540]) ).
cnf(c30,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)],[f16_sk]) ).
cnf(p121,plain,
( ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,sk0)
| ~ l3_lattices(sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[c30,c1]) ).
cnf(p122,plain,
( ~ v1_xboole_0(X0)
| ~ m2_filter_2(X0,sk0)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p121,c2]) ).
cnf(p125,plain,
( v3_struct_0(sk0)
| ~ v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p122,p111]) ).
cnf(p129,plain,
( ~ v1_xboole_0(u1_struct_0(sk0))
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p125]) ).
cnf(p2546,plain,
( v3_struct_0(sk0)
| v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(resolution,[status(thm)],[p2542,p129]) ).
cnf(p2549,plain,
( v1_xboole_0(sk1)
| v3_struct_0(sk0) ),
inference(factoring,[status(thm)],[p2546]) ).
fof(f48,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f48_nnf,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c71,plain,
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(p289,plain,
~ v1_xboole_0(sk1),
inference(resolution,[status(thm)],[c71,c5]) ).
cnf(p2552,plain,
v3_struct_0(sk0),
inference(resolution,[status(thm)],[p2549,p289]) ).
cnf(c0,plain,
~ v3_struct_0(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p2553,plain,
$false,
inference(resolution,[status(thm)],[p2552,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.38 % Computer : n013.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Wed Sep 23 21:01:04 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.58/11.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.58/11.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------