%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP641+1 : 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 07:30:37 AM UTC 2026
% Result : Theorem 0.15s 10.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 78 ( 20 unt; 0 def)
% Number of atoms : 281 ( 32 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 353 ( 150 ~; 146 |; 40 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(B) )
=> ( B = k1_latsubgr(A)
<=> ! [C] :
( ( m1_group_2(C,A)
& v1_group_1(C) )
=> k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ),
file('theBenchmark.p',d1_latsubgr) ).
fof(dt_k1_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) ) ),
file('theBenchmark.p',dt_k1_latsubgr) ).
fof(dt_k2_group_1,axiom,
! [A] :
( ( l1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_group_1(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k2_group_1) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_m1_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('theBenchmark.p',dt_m1_group_2) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t53_group_2,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> k2_group_1(B) = k2_group_1(A) ) ),
file('theBenchmark.p',t53_group_2) ).
fof(t19_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
file('theBenchmark.p',t19_latsubgr) ).
fof(t19_latsubgr_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
inference(assume_negation,[status(cth)],[t19_latsubgr]) ).
fof(nnf_54,plain,
? [A] :
( ? [B] :
( ~ r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B))
& m1_group_2(B,A)
& v1_group_1(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t19_latsubgr_neg]) ).
fof(sk_t19_latsubgr_neg,plain,
( ~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
& m1_group_2(sK1,sK0)
& v1_group_1(sK1)
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_54]) ).
cnf(c_55,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_latsubgr_neg]) ).
cnf(c_56,plain,
( k2_group_1(B) = k2_group_1(A)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t53_group_2]) ).
cnf(c_58,plain,
( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k1_latsubgr]) ).
cnf(c_59,plain,
( v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k1_latsubgr]) ).
cnf(c_60,plain,
( v1_funct_1(k1_latsubgr(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k1_latsubgr]) ).
cnf(c_64,plain,
( u1_struct_0(C) = k1_funct_1(B,C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| k1_latsubgr(A) != B
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[d1_latsubgr]) ).
cnf(c_66,negated_conjecture,
( u1_struct_0(B) = k1_funct_1(A,B)
| ~ m1_group_2(B,sK0)
| ~ v1_group_1(B)
| k1_latsubgr(sK0) != A
| ~ m2_relset_1(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_2(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_64]) ).
cnf(c_67,negated_conjecture,
v1_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t19_latsubgr_neg]) ).
cnf(c_73,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
cnf(c_75,plain,
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(clausify,[status(thm)],[dt_l1_group_1]) ).
cnf(c_88,negated_conjecture,
( u1_struct_0(sK1) = k1_funct_1(A,sK1)
| ~ m1_group_2(sK1,sK0)
| k1_latsubgr(sK0) != A
| ~ m2_relset_1(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_2(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_67,c_66]) ).
cnf(c_89,negated_conjecture,
( k1_funct_1(A,sK1) = u1_struct_0(sK1)
| ~ m1_group_2(sK1,sK0)
| k1_latsubgr(sK0) != A
| ~ m2_relset_1(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_2(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_95,plain,
( m1_subset_1(k2_group_1(A),u1_struct_0(A))
| ~ l1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k2_group_1]) ).
cnf(c_96,plain,
( ~ v3_struct_0(B)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m1_group_2]) ).
cnf(c_98,plain,
( l1_group_1(B)
| ~ m1_group_2(B,A)
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_m1_group_2]) ).
cnf(c_128,plain,
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_134,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_latsubgr_neg]) ).
cnf(c_135,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_latsubgr_neg]) ).
cnf(c_136,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_latsubgr_neg]) ).
cnf(c_137,negated_conjecture,
m1_group_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t19_latsubgr_neg]) ).
cnf(c_138,negated_conjecture,
~ r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_t19_latsubgr_neg]) ).
cnf(c_139,negated_conjecture,
( k2_group_1(A) = k2_group_1(sK0)
| ~ m1_group_2(A,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_56]) ).
cnf(c_619,negated_conjecture,
( k2_group_1(sK0) = k2_group_1(A)
| ~ m1_group_2(A,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(copy,[status(thm)],[c_139]) ).
cnf(c_620,negated_conjecture,
( k2_group_1(sK0) = k2_group_1(A)
| ~ m1_group_2(A,sK0)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_619]) ).
cnf(c_621,negated_conjecture,
( k2_group_1(sK0) = k2_group_1(A)
| ~ m1_group_2(A,sK0)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_135,c_620]) ).
cnf(c_140,negated_conjecture,
( k2_group_1(sK0) = k2_group_1(A)
| ~ m1_group_2(A,sK0) ),
inference(resolve,[status(thm)],[c_136,c_621]) ).
cnf(c_143,negated_conjecture,
( m2_relset_1(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_58]) ).
cnf(c_622,negated_conjecture,
( m2_relset_1(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_143]) ).
cnf(c_623,negated_conjecture,
( m2_relset_1(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_135,c_622]) ).
cnf(c_144,negated_conjecture,
m2_relset_1(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_136,c_623]) ).
cnf(c_145,negated_conjecture,
( v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_59]) ).
cnf(c_624,negated_conjecture,
( v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_145]) ).
cnf(c_625,negated_conjecture,
( v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_135,c_624]) ).
cnf(c_146,negated_conjecture,
v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_136,c_625]) ).
cnf(c_147,negated_conjecture,
( v1_funct_1(k1_latsubgr(sK0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_55,c_60]) ).
cnf(c_626,negated_conjecture,
( v1_funct_1(k1_latsubgr(sK0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_147]) ).
cnf(c_627,negated_conjecture,
( v1_funct_1(k1_latsubgr(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_135,c_626]) ).
cnf(c_148,negated_conjecture,
v1_funct_1(k1_latsubgr(sK0)),
inference(resolve,[status(thm)],[c_136,c_627]) ).
cnf(c_154,plain,
( ~ l1_group_1(A)
| ~ v1_xboole_0(u1_struct_0(A))
| v3_struct_0(A) ),
inference(resolve,[status(thm)],[c_73,c_75]) ).
cnf(c_628,negated_conjecture,
( k1_funct_1(A,sK1) = u1_struct_0(sK1)
| ~ m1_group_2(sK1,sK0)
| k1_latsubgr(sK0) != A
| ~ m2_relset_1(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_2(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_89]) ).
cnf(c_629,negated_conjecture,
( k1_funct_1(A,sK1) = u1_struct_0(sK1)
| ~ m1_group_2(sK1,sK0)
| k1_latsubgr(sK0) != A
| ~ m2_relset_1(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_2(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(A)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_135,c_628]) ).
cnf(c_630,negated_conjecture,
( k1_funct_1(A,sK1) = u1_struct_0(sK1)
| ~ m1_group_2(sK1,sK0)
| k1_latsubgr(sK0) != A
| ~ m2_relset_1(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_2(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(A) ),
inference(resolve,[status(thm)],[c_136,c_629]) ).
cnf(c_170,negated_conjecture,
( k1_funct_1(A,sK1) = u1_struct_0(sK1)
| k1_latsubgr(sK0) != A
| ~ m2_relset_1(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_2(A,k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(A) ),
inference(resolve,[status(thm)],[c_137,c_630]) ).
cnf(c_631,negated_conjecture,
( l1_group_1(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_137,c_98]) ).
cnf(c_632,negated_conjecture,
( l1_group_1(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_631]) ).
cnf(c_633,negated_conjecture,
( l1_group_1(sK1)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_135,c_632]) ).
cnf(c_232,negated_conjecture,
l1_group_1(sK1),
inference(resolve,[status(thm)],[c_136,c_633]) ).
cnf(c_634,negated_conjecture,
( ~ v3_struct_0(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_137,c_96]) ).
cnf(c_635,negated_conjecture,
( ~ v3_struct_0(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_634]) ).
cnf(c_636,negated_conjecture,
( ~ v3_struct_0(sK1)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_135,c_635]) ).
cnf(c_234,negated_conjecture,
~ v3_struct_0(sK1),
inference(resolve,[status(thm)],[c_136,c_636]) ).
cnf(c_637,negated_conjecture,
k2_group_1(sK0) = k2_group_1(sK1),
inference(resolve,[status(thm)],[c_140,c_137]) ).
cnf(c_236,negated_conjecture,
k2_group_1(sK1) = k2_group_1(sK0),
inference(copy,[status(thm)],[c_637]) ).
cnf(c_638,negated_conjecture,
( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| k1_latsubgr(sK0) != k1_latsubgr(sK0)
| ~ v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(k1_latsubgr(sK0)) ),
inference(resolve,[status(thm)],[c_170,c_144]) ).
cnf(c_639,negated_conjecture,
( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| ~ v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_funct_1(k1_latsubgr(sK0)) ),
inference(copy,[status(thm)],[c_638]) ).
cnf(c_640,negated_conjecture,
( k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1)
| ~ v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_148,c_639]) ).
cnf(c_301,negated_conjecture,
k1_funct_1(k1_latsubgr(sK0),sK1) = u1_struct_0(sK1),
inference(resolve,[status(thm)],[c_146,c_640]) ).
cnf(c_303,negated_conjecture,
~ r2_hidden(k2_group_1(sK0),u1_struct_0(sK1)),
inference(paramod,[status(thm)],[c_301,c_138]) ).
cnf(c_641,plain,
( m1_subset_1(k2_group_1(sK1),u1_struct_0(sK1))
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_232,c_95]) ).
cnf(c_642,plain,
( m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1))
| v3_struct_0(sK1) ),
inference(paramod,[status(thm)],[c_236,c_641]) ).
cnf(c_339,plain,
m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_234,c_642]) ).
cnf(c_643,plain,
( ~ l1_group_1(sK1)
| ~ v1_xboole_0(u1_struct_0(sK1)) ),
inference(resolve,[status(thm)],[c_154,c_234]) ).
cnf(c_341,plain,
~ v1_xboole_0(u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_643,c_232]) ).
cnf(c_644,plain,
( r2_hidden(A,u1_struct_0(sK1))
| ~ m1_subset_1(A,u1_struct_0(sK1)) ),
inference(resolve,[status(thm)],[c_128,c_341]) ).
cnf(c_645,negated_conjecture,
~ m1_subset_1(k2_group_1(sK0),u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_644,c_303]) ).
cnf(c_618,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_339,c_645]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP641+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n016.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Fri Sep 25 15:23:11 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.39 % Process 2740976 was started by sandbox on n016,
% 0.11/10.39 % Fri Sep 25 15:23:11 2026
% 0.11/10.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/10.39
% 0.11/10.39 % From the command line: assign(max_seconds, 300).
% 0.15/10.45
% 0.15/10.45 % SZS status Theorem for theBenchmark
% 0.15/10.45
% 0.15/10.45 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/10.45 % Length of proof is 48.
% 0.15/10.45 % Level of proof is 8.
% 0.15/10.45 % Maximum clause weight is 50.000.
% 0.15/10.45 % Given clauses 112.
% 0.15/10.45
% 0.15/10.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------