%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT319+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 : n006.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 07:50:12 AM UTC 2026
% Result : Theorem 0.73s 0.52s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 136 ( 16 unt; 0 def)
% Number of atoms : 582 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 699 ( 253 ~; 347 |; 84 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc5_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v17_lattices(A)
& ~ v3_struct_0(A) )
=> ( v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc5_lattices) ).
fof(cc6_lattices,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v16_lattices(A)
& v15_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) )
=> ( v17_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('theBenchmark.p',cc6_lattices) ).
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(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(t53_filter_2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( ( l3_lattices(A)
& v16_lattices(A)
& v15_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
<=> ( l3_lattices(k1_lattice2(A))
& v16_lattices(k1_lattice2(A))
& v15_lattices(k1_lattice2(A))
& v10_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ) ),
file('theBenchmark.p',t53_filter_2) ).
fof(t65_lattice2,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( ( l3_lattices(A)
& v11_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
<=> ( l3_lattices(k1_lattice2(A))
& v11_lattices(k1_lattice2(A))
& v10_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ) ),
file('theBenchmark.p',t65_lattice2) ).
fof(t54_filter_2,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( ( l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
<=> ( l3_lattices(k1_lattice2(A))
& v17_lattices(k1_lattice2(A))
& v10_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ) ),
file('theBenchmark.p',t54_filter_2) ).
fof(t54_filter_2_neg,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( ( l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
<=> ( l3_lattices(k1_lattice2(A))
& v17_lattices(k1_lattice2(A))
& v10_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ) ),
inference(assume_negation,[status(cth)],[t54_filter_2]) ).
cnf(c_213,plain,
( v11_lattices(A)
| ~ v17_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[cc5_lattices]) ).
cnf(c_215,plain,
( v15_lattices(A)
| ~ v17_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[cc5_lattices]) ).
cnf(c_216,plain,
( v16_lattices(A)
| ~ v17_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[cc5_lattices]) ).
cnf(c_217,plain,
( v17_lattices(A)
| ~ v16_lattices(A)
| ~ v15_lattices(A)
| ~ v11_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[cc6_lattices]) ).
cnf(c_220,plain,
( l3_lattices(k1_lattice2(A))
| ~ l3_lattices(A) ),
inference(clausify,[status(thm)],[dt_k1_lattice2]) ).
cnf(c_224,plain,
( ~ v3_struct_0(k1_lattice2(A))
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_lattice2]) ).
cnf(c_234,plain,
( v10_lattices(k1_lattice2(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc6_lattice2]) ).
cnf(c_307,plain,
( v15_lattices(k1_lattice2(A))
| ~ v16_lattices(A)
| ~ v15_lattices(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t53_filter_2]) ).
cnf(c_308,plain,
( v16_lattices(k1_lattice2(A))
| ~ v16_lattices(A)
| ~ v15_lattices(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t53_filter_2]) ).
cnf(c_309,plain,
( ~ l3_lattices(k1_lattice2(A))
| ~ v16_lattices(k1_lattice2(A))
| ~ v15_lattices(k1_lattice2(A))
| ~ v10_lattices(k1_lattice2(A))
| v3_struct_0(k1_lattice2(A))
| v15_lattices(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t53_filter_2]) ).
cnf(c_310,plain,
( ~ l3_lattices(k1_lattice2(A))
| ~ v16_lattices(k1_lattice2(A))
| ~ v15_lattices(k1_lattice2(A))
| ~ v10_lattices(k1_lattice2(A))
| v3_struct_0(k1_lattice2(A))
| v16_lattices(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t53_filter_2]) ).
cnf(c_312,plain,
( v11_lattices(k1_lattice2(A))
| ~ v11_lattices(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t65_lattice2]) ).
cnf(c_313,plain,
( ~ l3_lattices(k1_lattice2(A))
| ~ v11_lattices(k1_lattice2(A))
| ~ v10_lattices(k1_lattice2(A))
| v3_struct_0(k1_lattice2(A))
| v11_lattices(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t65_lattice2]) ).
fof(nnf_76,plain,
? [A] :
( ( ~ l3_lattices(k1_lattice2(A))
| ~ v17_lattices(k1_lattice2(A))
| ~ v10_lattices(k1_lattice2(A))
| v3_struct_0(k1_lattice2(A))
| ~ l3_lattices(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) )
& ( ( l3_lattices(k1_lattice2(A))
& v17_lattices(k1_lattice2(A))
& v10_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ( l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t54_filter_2_neg]) ).
fof(sk_t54_filter_2_neg_sk,plain,
( ( ~ l3_lattices(k1_lattice2(sK0))
| ~ v17_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v17_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0) )
& ( ( l3_lattices(k1_lattice2(sK0))
& v17_lattices(k1_lattice2(sK0))
& v10_lattices(k1_lattice2(sK0))
& ~ v3_struct_0(k1_lattice2(sK0)) )
| ( l3_lattices(sK0)
& v17_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ) )
& l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_76]) ).
fof(sk_t54_filter_2_neg,plain,
( ( ~ l3_lattices(k1_lattice2(sK0))
| ~ v17_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v17_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0) )
& ( l3_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) )
& ( v17_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) )
& ( v10_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) )
& ( ~ v3_struct_0(k1_lattice2(sK0))
| v17_lattices(sK0) )
& l3_lattices(sK0)
& v10_lattices(sK0)
& ~ v3_struct_0(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t54_filter_2_neg_sk]) ).
cnf(c_317,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t54_filter_2_neg]) ).
cnf(c_318,negated_conjecture,
v10_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t54_filter_2_neg]) ).
cnf(c_319,negated_conjecture,
l3_lattices(sK0),
inference(split_conjunct,[status(thm)],[sk_t54_filter_2_neg]) ).
cnf(c_320,negated_conjecture,
( ~ v3_struct_0(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t54_filter_2_neg]) ).
cnf(c_322,negated_conjecture,
( v17_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t54_filter_2_neg]) ).
cnf(c_324,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v17_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v17_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t54_filter_2_neg]) ).
cnf(c_1183,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v17_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v17_lattices(sK0)
| ~ v10_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_324]) ).
cnf(c_1184,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v17_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_318,c_1183]) ).
cnf(c_325,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v17_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_319,c_1184]) ).
cnf(c_1185,negated_conjecture,
( v10_lattices(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_318,c_234]) ).
cnf(c_1186,negated_conjecture,
( v10_lattices(k1_lattice2(sK0))
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_1185]) ).
cnf(c_503,negated_conjecture,
v10_lattices(k1_lattice2(sK0)),
inference(resolve,[status(thm)],[c_319,c_1186]) ).
cnf(c_514,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v17_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_503,c_325]) ).
cnf(c_515,plain,
l3_lattices(k1_lattice2(sK0)),
inference(resolve,[status(thm)],[c_319,c_220]) ).
cnf(c_522,negated_conjecture,
( ~ v17_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_515,c_514]) ).
cnf(c_1187,negated_conjecture,
( v11_lattices(sK0)
| v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_322,c_213]) ).
cnf(c_1188,negated_conjecture,
( v11_lattices(sK0)
| v3_struct_0(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1187]) ).
cnf(c_526,negated_conjecture,
( v11_lattices(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1188]) ).
cnf(c_1189,negated_conjecture,
( v16_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_322,c_216]) ).
cnf(c_527,negated_conjecture,
( v16_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_515,c_1189]) ).
cnf(c_1190,negated_conjecture,
( v15_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_322,c_215]) ).
cnf(c_528,negated_conjecture,
( v15_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_515,c_1190]) ).
cnf(c_1191,plain,
( v11_lattices(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_526,c_312]) ).
cnf(c_1192,negated_conjecture,
( v11_lattices(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1191]) ).
cnf(c_1193,negated_conjecture,
( v11_lattices(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_318,c_1192]) ).
cnf(c_897,negated_conjecture,
( v11_lattices(k1_lattice2(sK0))
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1193]) ).
cnf(c_1194,plain,
( v11_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(k1_lattice2(sK0))
| v11_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_897,c_213]) ).
cnf(c_1195,plain,
( v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(k1_lattice2(sK0))
| v11_lattices(k1_lattice2(sK0)) ),
inference(copy,[status(thm)],[c_1194]) ).
cnf(c_996,plain,
( v3_struct_0(k1_lattice2(sK0))
| v11_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_515,c_1195]) ).
cnf(c_1196,plain,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v11_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_996,c_313]) ).
cnf(c_1197,plain,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v11_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v3_struct_0(k1_lattice2(sK0)) ),
inference(copy,[status(thm)],[c_1196]) ).
cnf(c_1198,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v11_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1197]) ).
cnf(c_1199,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v11_lattices(sK0)
| ~ l3_lattices(sK0)
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_318,c_1198]) ).
cnf(c_1200,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v11_lattices(sK0)
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1199]) ).
cnf(c_1201,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| v11_lattices(sK0)
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_503,c_1200]) ).
cnf(c_1003,negated_conjecture,
( v11_lattices(sK0)
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_515,c_1201]) ).
cnf(c_1202,plain,
( ~ l3_lattices(sK0)
| v3_struct_0(sK0)
| v11_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_996,c_224]) ).
cnf(c_1203,negated_conjecture,
( ~ l3_lattices(sK0)
| v11_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1202]) ).
cnf(c_1006,negated_conjecture,
v11_lattices(k1_lattice2(sK0)),
inference(resolve,[status(thm)],[c_319,c_1203]) ).
cnf(c_1204,plain,
( ~ l3_lattices(sK0)
| v3_struct_0(sK0)
| v11_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1003,c_224]) ).
cnf(c_1205,negated_conjecture,
( ~ l3_lattices(sK0)
| v11_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_1204]) ).
cnf(c_1008,negated_conjecture,
v11_lattices(sK0),
inference(resolve,[status(thm)],[c_319,c_1205]) ).
cnf(c_1206,negated_conjecture,
( v17_lattices(sK0)
| v16_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_527,c_320]) ).
cnf(c_1060,negated_conjecture,
( v16_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(copy,[status(thm)],[c_1206]) ).
cnf(c_1207,plain,
( v16_lattices(sK0)
| v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1060,c_216]) ).
cnf(c_1208,negated_conjecture,
( v16_lattices(sK0)
| v3_struct_0(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1207]) ).
cnf(c_1065,negated_conjecture,
( v16_lattices(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1208]) ).
cnf(c_1209,plain,
( v15_lattices(sK0)
| v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1060,c_215]) ).
cnf(c_1210,negated_conjecture,
( v15_lattices(sK0)
| v3_struct_0(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1209]) ).
cnf(c_1066,negated_conjecture,
( v15_lattices(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1210]) ).
cnf(c_1211,plain,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v16_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1065,c_310]) ).
cnf(c_1212,plain,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v16_lattices(sK0) ),
inference(copy,[status(thm)],[c_1211]) ).
cnf(c_1213,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_1212]) ).
cnf(c_1214,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_318,c_1213]) ).
cnf(c_1215,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_319,c_1214]) ).
cnf(c_1216,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_503,c_1215]) ).
cnf(c_1086,negated_conjecture,
( ~ v15_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_515,c_1216]) ).
cnf(c_1217,plain,
( v16_lattices(k1_lattice2(sK0))
| ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1065,c_308]) ).
cnf(c_1218,plain,
( ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(copy,[status(thm)],[c_1217]) ).
cnf(c_1219,negated_conjecture,
( ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1218]) ).
cnf(c_1220,negated_conjecture,
( ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_318,c_1219]) ).
cnf(c_1087,negated_conjecture,
( ~ v15_lattices(sK0)
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1220]) ).
cnf(c_1221,plain,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v15_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1066,c_309]) ).
cnf(c_1222,plain,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v15_lattices(sK0) ),
inference(copy,[status(thm)],[c_1221]) ).
cnf(c_1223,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_1222]) ).
cnf(c_1224,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(sK0)
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_318,c_1223]) ).
cnf(c_1225,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v10_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_319,c_1224]) ).
cnf(c_1226,negated_conjecture,
( ~ l3_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_503,c_1225]) ).
cnf(c_1088,negated_conjecture,
( ~ v15_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_515,c_1226]) ).
cnf(c_1227,plain,
( v16_lattices(k1_lattice2(sK0))
| v16_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1087,c_1066]) ).
cnf(c_1091,plain,
v16_lattices(k1_lattice2(sK0)),
inference(copy,[status(thm)],[c_1227]) ).
cnf(c_1228,plain,
( v17_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v11_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0))
| ~ l3_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1091,c_217]) ).
cnf(c_1229,plain,
( v17_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| ~ v11_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_515,c_1228]) ).
cnf(c_1094,plain,
( v17_lattices(k1_lattice2(sK0))
| ~ v15_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1006,c_1229]) ).
cnf(c_1230,negated_conjecture,
( v17_lattices(sK0)
| v15_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(resolve,[status(thm)],[c_528,c_320]) ).
cnf(c_1095,negated_conjecture,
( v15_lattices(k1_lattice2(sK0))
| v17_lattices(sK0) ),
inference(copy,[status(thm)],[c_1230]) ).
cnf(c_1231,plain,
( v16_lattices(sK0)
| v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1095,c_216]) ).
cnf(c_1232,negated_conjecture,
( v16_lattices(sK0)
| v3_struct_0(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1231]) ).
cnf(c_1140,negated_conjecture,
( v16_lattices(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1232]) ).
cnf(c_1233,plain,
( v15_lattices(sK0)
| v3_struct_0(sK0)
| ~ l3_lattices(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1095,c_215]) ).
cnf(c_1234,negated_conjecture,
( v15_lattices(sK0)
| v3_struct_0(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1233]) ).
cnf(c_1141,negated_conjecture,
( v15_lattices(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1234]) ).
cnf(c_1235,plain,
( v15_lattices(k1_lattice2(sK0))
| ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1140,c_307]) ).
cnf(c_1236,plain,
( ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v3_struct_0(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(copy,[status(thm)],[c_1235]) ).
cnf(c_1237,negated_conjecture,
( ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| ~ v10_lattices(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1236]) ).
cnf(c_1238,negated_conjecture,
( ~ v15_lattices(sK0)
| ~ l3_lattices(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_318,c_1237]) ).
cnf(c_1143,negated_conjecture,
( ~ v15_lattices(sK0)
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_319,c_1238]) ).
cnf(c_1239,plain,
( v15_lattices(k1_lattice2(sK0))
| v15_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1143,c_1141]) ).
cnf(c_1144,plain,
v15_lattices(k1_lattice2(sK0)),
inference(copy,[status(thm)],[c_1239]) ).
cnf(c_1145,plain,
( v17_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1144,c_1094]) ).
cnf(c_1148,negated_conjecture,
( v3_struct_0(k1_lattice2(sK0))
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1144,c_1088]) ).
cnf(c_1149,negated_conjecture,
( v3_struct_0(k1_lattice2(sK0))
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1144,c_1086]) ).
cnf(c_1240,plain,
( ~ l3_lattices(sK0)
| v3_struct_0(sK0)
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1148,c_224]) ).
cnf(c_1241,negated_conjecture,
( ~ l3_lattices(sK0)
| v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_1240]) ).
cnf(c_1172,negated_conjecture,
v15_lattices(sK0),
inference(resolve,[status(thm)],[c_319,c_1241]) ).
cnf(c_1242,plain,
( ~ l3_lattices(sK0)
| v3_struct_0(sK0)
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1149,c_224]) ).
cnf(c_1243,negated_conjecture,
( ~ l3_lattices(sK0)
| v16_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_1242]) ).
cnf(c_1176,negated_conjecture,
v16_lattices(sK0),
inference(resolve,[status(thm)],[c_319,c_1243]) ).
cnf(c_1244,plain,
( v17_lattices(sK0)
| ~ v15_lattices(sK0)
| ~ v11_lattices(sK0)
| v3_struct_0(sK0)
| ~ l3_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1176,c_217]) ).
cnf(c_1245,negated_conjecture,
( v17_lattices(sK0)
| ~ v15_lattices(sK0)
| ~ v11_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_319,c_1244]) ).
cnf(c_1246,negated_conjecture,
( v17_lattices(sK0)
| ~ v15_lattices(sK0)
| ~ v11_lattices(sK0) ),
inference(resolve,[status(thm)],[c_317,c_1245]) ).
cnf(c_1247,negated_conjecture,
( v17_lattices(sK0)
| ~ v15_lattices(sK0) ),
inference(resolve,[status(thm)],[c_1008,c_1246]) ).
cnf(c_1177,negated_conjecture,
v17_lattices(sK0),
inference(resolve,[status(thm)],[c_1172,c_1247]) ).
cnf(c_1178,negated_conjecture,
( ~ v17_lattices(k1_lattice2(sK0))
| v3_struct_0(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1177,c_522]) ).
cnf(c_1248,plain,
( ~ l3_lattices(sK0)
| v3_struct_0(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_1145,c_224]) ).
cnf(c_1249,negated_conjecture,
( ~ l3_lattices(sK0)
| v17_lattices(k1_lattice2(sK0)) ),
inference(resolve,[status(thm)],[c_317,c_1248]) ).
cnf(c_1180,negated_conjecture,
v17_lattices(k1_lattice2(sK0)),
inference(resolve,[status(thm)],[c_319,c_1249]) ).
cnf(c_1181,negated_conjecture,
v3_struct_0(k1_lattice2(sK0)),
inference(resolve,[status(thm)],[c_1180,c_1178]) ).
cnf(c_1250,negated_conjecture,
( ~ l3_lattices(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_1181,c_224]) ).
cnf(c_1251,negated_conjecture,
~ l3_lattices(sK0),
inference(resolve,[status(thm)],[c_317,c_1250]) ).
cnf(c_1182,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_319,c_1251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT319+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 20:49:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3688031 was started by sandbox2 on n006,
% 0.09/0.36 % Fri Sep 25 20:49:41 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.73/0.52
% 0.73/0.52 % SZS status Theorem for theBenchmark
% 0.73/0.52
% 0.73/0.52 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.73/0.52 % Length of proof is 63.
% 0.73/0.52 % Level of proof is 13.
% 0.73/0.52 % Maximum clause weight is 33.000.
% 0.73/0.52 % Given clauses 390.
% 0.73/0.52
% 0.73/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------