%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP642+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 : n003.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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 18 unt; 0 def)
% Number of atoms : 238 ( 32 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 307 ( 133 ~; 125 |; 36 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 12 !; 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_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(t20_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) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
file('theBenchmark.p',t20_latsubgr) ).
fof(t20_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) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
inference(assume_negation,[status(cth)],[t20_latsubgr]) ).
fof(nnf_52,plain,
? [A] :
( ? [B] :
( k1_funct_1(k1_latsubgr(A),B) = k1_xboole_0
& 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)],[t20_latsubgr_neg]) ).
fof(sk_t20_latsubgr_neg,plain,
( k1_funct_1(k1_latsubgr(sK0),sK1) = k1_xboole_0
& 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_52]) ).
cnf(c_53,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_55,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_56,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_57,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_61,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_63,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_53,c_61]) ).
cnf(c_64,negated_conjecture,
v1_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_70,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_72,plain,
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(clausify,[status(thm)],[dt_l1_group_1]) ).
cnf(c_85,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_64,c_63]) ).
cnf(c_86,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_85]) ).
cnf(c_92,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_94,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]) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_105,plain,
v1_xboole_0(k1_xboole_0),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_130,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_131,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_132,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_133,negated_conjecture,
m1_group_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_134,negated_conjecture,
k1_funct_1(k1_latsubgr(sK0),sK1) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_137,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_53,c_55]) ).
cnf(c_329,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_130,c_137]) ).
cnf(c_330,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_131,c_329]) ).
cnf(c_138,negated_conjecture,
m2_relset_1(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_132,c_330]) ).
cnf(c_139,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_53,c_56]) ).
cnf(c_331,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_130,c_139]) ).
cnf(c_332,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_131,c_331]) ).
cnf(c_140,negated_conjecture,
v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0))),
inference(resolve,[status(thm)],[c_132,c_332]) ).
cnf(c_141,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_53,c_57]) ).
cnf(c_333,negated_conjecture,
( v1_funct_1(k1_latsubgr(sK0))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_130,c_141]) ).
cnf(c_334,negated_conjecture,
( v1_funct_1(k1_latsubgr(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_131,c_333]) ).
cnf(c_142,negated_conjecture,
v1_funct_1(k1_latsubgr(sK0)),
inference(resolve,[status(thm)],[c_132,c_334]) ).
cnf(c_148,plain,
( ~ l1_group_1(A)
| ~ v1_xboole_0(u1_struct_0(A))
| v3_struct_0(A) ),
inference(resolve,[status(thm)],[c_70,c_72]) ).
cnf(c_335,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_130,c_86]) ).
cnf(c_336,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_131,c_335]) ).
cnf(c_337,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_132,c_336]) ).
cnf(c_164,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_133,c_337]) ).
cnf(c_338,negated_conjecture,
( l1_group_1(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_133,c_94]) ).
cnf(c_339,negated_conjecture,
( l1_group_1(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_130,c_338]) ).
cnf(c_340,negated_conjecture,
( l1_group_1(sK1)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_131,c_339]) ).
cnf(c_224,negated_conjecture,
l1_group_1(sK1),
inference(resolve,[status(thm)],[c_132,c_340]) ).
cnf(c_341,negated_conjecture,
( ~ v3_struct_0(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_133,c_92]) ).
cnf(c_342,negated_conjecture,
( ~ v3_struct_0(sK1)
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_130,c_341]) ).
cnf(c_343,negated_conjecture,
( ~ v3_struct_0(sK1)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_131,c_342]) ).
cnf(c_226,negated_conjecture,
~ v3_struct_0(sK1),
inference(resolve,[status(thm)],[c_132,c_343]) ).
cnf(c_344,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_164,c_138]) ).
cnf(c_345,negated_conjecture,
( k1_xboole_0 = 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(paramod,[status(thm)],[c_134,c_344]) ).
cnf(c_346,negated_conjecture,
( u1_struct_0(sK1) = k1_xboole_0
| 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(copy,[status(thm)],[c_345]) ).
cnf(c_347,negated_conjecture,
( u1_struct_0(sK1) = k1_xboole_0
| ~ 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_346]) ).
cnf(c_348,negated_conjecture,
( u1_struct_0(sK1) = k1_xboole_0
| ~ v1_funct_2(k1_latsubgr(sK0),k1_group_3(sK0),k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_142,c_347]) ).
cnf(c_293,negated_conjecture,
u1_struct_0(sK1) = k1_xboole_0,
inference(resolve,[status(thm)],[c_140,c_348]) ).
cnf(c_349,plain,
( ~ l1_group_1(sK1)
| ~ v1_xboole_0(u1_struct_0(sK1)) ),
inference(resolve,[status(thm)],[c_148,c_226]) ).
cnf(c_350,plain,
~ v1_xboole_0(u1_struct_0(sK1)),
inference(resolve,[status(thm)],[c_349,c_224]) ).
cnf(c_351,plain,
~ v1_xboole_0(k1_xboole_0),
inference(paramod,[status(thm)],[c_293,c_350]) ).
cnf(c_328,plain,
$false,
inference(resolve,[status(thm)],[c_105,c_351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 15:21:08 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 512973 was started by sandbox2 on n003,
% 0.10/0.35 % Fri Sep 25 15:21:08 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.39 % Length of proof is 37.
% 0.13/0.39 % Level of proof is 7.
% 0.13/0.39 % Maximum clause weight is 41.000.
% 0.13/0.39 % Given clauses 80.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------