%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT300+3 : 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 : n016.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 07:50:06 AM UTC 2026
% Result : Theorem 32.47s 10.28s
% Output : CNFRefutation 32.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 183 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 206 ( 77 ~; 75 |; 40 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('theBenchmark.p',fc1_lattice2) ).
fof(fc6_lattice2,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('theBenchmark.p',fc6_lattice2) ).
fof(t18_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( u1_lattices(A) = u2_lattices(k1_lattice2(A))
& u2_lattices(A) = u1_lattices(k1_lattice2(A))
& u1_struct_0(A) = u1_struct_0(k1_lattice2(A)) ) ),
file('theBenchmark.p',t18_lattice2) ).
fof(dt_k1_lattice2,axiom,
! [A] :
( l3_lattices(A)
=> ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) ) ),
file('theBenchmark.p',dt_k1_lattice2) ).
fof(redefinition_m1_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_2(B,A)
<=> m1_filter_0(B,A) ) ),
file('theBenchmark.p',redefinition_m1_filter_2) ).
fof(t11_filter_0,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_filter_0(B,A)
=> ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(A)) ) ) ),
file('theBenchmark.p',t11_filter_0) ).
fof(t21_filter_2,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('theBenchmark.p',t21_filter_2) ).
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]) ).
fof(nnf_257,plain,
! [A] :
( ! [B] :
( ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_filter_0(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t11_filter_0]) ).
fof(sk_t11_filter_0_sk,plain,
! [A] :
( ! [B] :
( ( r2_hidden(sK0(A,B),B)
& m1_subset_1(sK0(A,B),u1_struct_0(A)) )
| ~ m1_filter_0(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_257]) ).
fof(sk_t11_filter_0,plain,
( ! [VAR_0,VAR_1] :
( r2_hidden(sK0(VAR_0,VAR_1),VAR_1)
| ~ m1_filter_0(VAR_1,VAR_0)
| ~ l3_lattices(VAR_0)
| ~ v10_lattices(VAR_0)
| v3_struct_0(VAR_0) )
& ! [VAR_0,VAR_1] :
( m1_subset_1(sK0(VAR_0,VAR_1),u1_struct_0(VAR_0))
| ~ m1_filter_0(VAR_1,VAR_0)
| ~ l3_lattices(VAR_0)
| ~ v10_lattices(VAR_0)
| v3_struct_0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t11_filter_0_sk]) ).
cnf(c_816,plain,
( m1_subset_1(sK0(A,B),u1_struct_0(A))
| ~ m1_filter_0(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(split_conjunct,[status(thm)],[sk_t11_filter_0]) ).
cnf(c_817,plain,
( r2_hidden(sK0(A,B),B)
| ~ m1_filter_0(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(split_conjunct,[status(thm)],[sk_t11_filter_0]) ).
cnf(c_986,plain,
( m1_filter_2(B,k1_lattice2(A))
| ~ m2_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t21_filter_2]) ).
cnf(c_1123,plain,
( ~ v3_struct_0(k1_lattice2(A))
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_lattice2]) ).
cnf(c_1131,plain,
( v10_lattices(k1_lattice2(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc6_lattice2]) ).
cnf(c_1134,plain,
( u1_struct_0(k1_lattice2(A)) = u1_struct_0(A)
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t18_lattice2]) ).
cnf(c_1159,plain,
( l3_lattices(k1_lattice2(A))
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[dt_k1_lattice2]) ).
cnf(c_1176,plain,
( m1_filter_0(B,A)
| ~ m1_filter_2(B,A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[redefinition_m1_filter_2]) ).
fof(nnf_339,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,sK2)
| ~ m1_subset_1(C,u1_struct_0(sK1)) )
& m2_filter_2(sK2,sK1)
& l3_lattices(sK1)
& v10_lattices(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_339]) ).
cnf(c_1239,negated_conjecture,
~ v3_struct_0(sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1240,negated_conjecture,
v10_lattices(sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1241,negated_conjecture,
l3_lattices(sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1242,negated_conjecture,
m2_filter_2(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_1243,negated_conjecture,
( ~ r2_hidden(A,sK2)
| ~ m1_subset_1(A,u1_struct_0(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t24_filter_2_neg]) ).
cnf(c_17396,negated_conjecture,
( m1_filter_2(sK2,k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1242,c_986]) ).
cnf(c_17397,negated_conjecture,
( m1_filter_2(sK2,k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| ~ v10_lattices(sK1) ),
inference(resolve,[status(thm)],[c_1239,c_17396]) ).
cnf(c_17398,negated_conjecture,
( m1_filter_2(sK2,k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(resolve,[status(thm)],[c_1240,c_17397]) ).
cnf(c_1475,negated_conjecture,
m1_filter_2(sK2,k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1241,c_17398]) ).
cnf(c_17399,negated_conjecture,
( ~ v3_struct_0(k1_lattice2(sK1))
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1123,c_1241]) ).
cnf(c_12600,negated_conjecture,
~ v3_struct_0(k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1239,c_17399]) ).
cnf(c_17400,negated_conjecture,
( v10_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1131,c_1240]) ).
cnf(c_17401,negated_conjecture,
( v10_lattices(k1_lattice2(sK1))
| ~ l3_lattices(sK1) ),
inference(resolve,[status(thm)],[c_1239,c_17400]) ).
cnf(c_12691,negated_conjecture,
v10_lattices(k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1241,c_17401]) ).
cnf(c_17402,negated_conjecture,
( u1_struct_0(k1_lattice2(sK1)) = u1_struct_0(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_1134,c_1241]) ).
cnf(c_12930,negated_conjecture,
u1_struct_0(k1_lattice2(sK1)) = u1_struct_0(sK1),
inference(resolve,[status(thm)],[c_1239,c_17402]) ).
cnf(c_14701,plain,
l3_lattices(k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_1159,c_1241]) ).
cnf(c_17403,plain,
( m1_filter_0(sK2,k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_1176,c_1475]) ).
cnf(c_17404,plain,
( m1_filter_0(sK2,k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_12600,c_17403]) ).
cnf(c_17405,plain,
( m1_filter_0(sK2,k1_lattice2(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_12691,c_17404]) ).
cnf(c_15953,plain,
m1_filter_0(sK2,k1_lattice2(sK1)),
inference(resolve,[status(thm)],[c_14701,c_17405]) ).
cnf(c_17406,plain,
( r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_15953,c_817]) ).
cnf(c_17407,plain,
( r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2)
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_12600,c_17406]) ).
cnf(c_17408,plain,
( r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2)
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_12691,c_17407]) ).
cnf(c_16020,plain,
r2_hidden(sK0(k1_lattice2(sK1),sK2),sK2),
inference(resolve,[status(thm)],[c_14701,c_17408]) ).
cnf(c_17409,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(k1_lattice2(sK1)))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_15953,c_816]) ).
cnf(c_17410,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1))
| v3_struct_0(k1_lattice2(sK1)) ),
inference(paramod,[status(thm)],[c_12930,c_17409]) ).
cnf(c_17411,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1))
| ~ l3_lattices(k1_lattice2(sK1))
| ~ v10_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_12600,c_17410]) ).
cnf(c_17412,plain,
( m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1))
| ~ l3_lattices(k1_lattice2(sK1)) ),
inference(resolve,[status(thm)],[c_12691,c_17411]) ).
cnf(c_16021,plain,
m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_14701,c_17412]) ).
cnf(c_17413,negated_conjecture,
~ m1_subset_1(sK0(k1_lattice2(sK1),sK2),u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_16020,c_1243]) ).
cnf(c_17395,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_16021,c_17413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT300+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.39 % Computer : n016.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Fri Sep 25 20:42:14 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 3232748 was started by sandbox on n016,
% 0.10/5.39 % Fri Sep 25 20:42:14 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 32.47/10.28
% 32.47/10.28 % SInE (scan): 208 to sos (tol 1.5x), 132 to usable (tol 2.0x), 13266 zapped, of 13606 axioms (depth 3).
% 32.47/10.28
% 32.47/10.28 % From the command line: assign(max_seconds, 300).
% 32.47/10.28
% 32.47/10.28 % given #500 (W,wt=7): 4915 v1_relat_1(f3(f79(A))) | v1_xboole_0(f79(A)). [resolve(3943,a,649,a)].
% 32.47/10.28
% 32.47/10.28 % given #1000 (F,wt=8): 11146 -r2_hidden(A,k1_relat_1(f52(k1_zfmisc_1(k2_zfmisc_1(A,B))))). [resolve(3587,a,408,b)].
% 32.47/10.28
% 32.47/10.28 % given #1500 (T,wt=5): 14655 v3_lattices(k1_lattice2(k8_filter_1(c12,c15))). [resolve(1158,a,6813,a)].
% 32.47/10.28
% 32.47/10.28 % SZS status Theorem for theBenchmark
% 32.47/10.28
% 32.47/10.28 % Proof 1 at 3.94 (+ 0.66) seconds.
% 32.47/10.28 % Length of proof is 30.
% 32.47/10.28 % Level of proof is 5.
% 32.47/10.28 % Maximum clause weight is 112.000.
% 32.47/10.28 % Given clauses 1982.
% 32.47/10.28
% 32.47/10.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------