%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP639+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 : n002.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 07:30:36 AM UTC 2026
% Result : Theorem 0.80s 0.53s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 19 unt; 0 def)
% Number of atoms : 214 ( 14 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 249 ( 93 ~; 82 |; 53 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 89 ( 4 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d5_group_4,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( m1_group_2(C,A)
& v1_group_1(C) )
=> ( C = k5_group_4(A,B)
<=> ( ! [D] :
( ( m1_group_2(D,A)
& v1_group_1(D) )
=> ( r1_tarski(B,u1_struct_0(D))
=> m1_group_2(C,D) ) )
& r1_tarski(B,u1_struct_0(C)) ) ) ) ) ),
file('theBenchmark.p',d5_group_4) ).
fof(dt_k5_group_4,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k5_group_4(A,B),A)
& v1_group_1(k5_group_4(A,B)) ) ),
file('theBenchmark.p',dt_k5_group_4) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_k2_funct_2,axiom,
! [A,B,C,D] :
( ( m1_relset_1(C,A,B)
& v1_funct_2(C,A,B)
& v1_funct_1(C) )
=> k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ),
file('theBenchmark.p',redefinition_k2_funct_2) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t156_relat_1,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( r1_tarski(A,B)
=> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ),
file('theBenchmark.p',t156_relat_1) ).
fof(t12_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D)))) ) ) ) ),
file('theBenchmark.p',t12_latsubgr) ).
fof(t12_latsubgr_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D)))) ) ) ) ),
inference(assume_negation,[status(cth)],[t12_latsubgr]) ).
fof(nnf_53,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ~ r1_tarski(k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(k5_group_4(A,D))))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(C) )
& l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t12_latsubgr_neg]) ).
fof(sk_t12_latsubgr_neg,plain,
( ~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK2),sK1,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK2),sK1,u1_struct_0(k5_group_4(sK0,sK3))))
& m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0)))
& m2_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK2))
& v1_funct_2(sK1,u1_struct_0(sK0),u1_struct_0(sK2))
& v1_funct_1(sK1)
& l1_group_1(sK2)
& v4_group_1(sK2)
& v3_group_1(sK2)
& ~ v3_struct_0(sK2)
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1,sK3]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK1),skolemize(D,sK3)],[nnf_53]) ).
cnf(c_54,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_55,plain,
( m1_group_2(k5_group_4(A,B),A)
| ~ m1_subset_1(B,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_k5_group_4]) ).
cnf(c_56,plain,
( v1_group_1(k5_group_4(A,B))
| ~ m1_subset_1(B,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_k5_group_4]) ).
cnf(c_62,plain,
( r1_tarski(B,u1_struct_0(C))
| k5_group_4(A,B) != C
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| ~ m1_subset_1(B,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)],[d5_group_4]) ).
cnf(c_64,plain,
( k9_relat_1(A,D) = k2_funct_2(B,C,A,D)
| ~ m1_relset_1(A,B,C)
| ~ v1_funct_2(A,B,C)
| ~ v1_funct_1(A) ),
inference(clausify,[status(thm)],[redefinition_k2_funct_2]) ).
cnf(c_65,negated_conjecture,
v1_funct_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_79,plain,
( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C)))
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_81,plain,
( m1_relset_1(A,B,C)
| ~ m2_relset_1(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_83,negated_conjecture,
m2_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK2)),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_85,plain,
( r1_tarski(k9_relat_1(A,B),k9_relat_1(A,C))
| ~ r1_tarski(B,C)
| ~ v1_relat_1(A) ),
inference(clausify,[status(thm)],[t156_relat_1]) ).
cnf(c_87,plain,
( v1_relat_1(A)
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_103,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(sK0),u1_struct_0(sK2)))),
inference(resolve,[status(thm)],[c_83,c_79]) ).
cnf(c_104,negated_conjecture,
m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK2)),
inference(resolve,[status(thm)],[c_83,c_81]) ).
cnf(c_118,negated_conjecture,
( r1_tarski(A,u1_struct_0(B))
| k5_group_4(sK0,A) != B
| ~ m1_group_2(B,sK0)
| ~ v1_group_1(B)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_54,c_62]) ).
cnf(c_124,negated_conjecture,
( v1_group_1(k5_group_4(sK0,A))
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_54,c_56]) ).
cnf(c_125,negated_conjecture,
( m1_group_2(k5_group_4(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_54,c_55]) ).
cnf(c_126,negated_conjecture,
~ r1_tarski(k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK2),sK1,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK2),sK1,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_127,negated_conjecture,
m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK0))),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_128,negated_conjecture,
v1_funct_2(sK1,u1_struct_0(sK0),u1_struct_0(sK2)),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_132,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_133,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_134,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_latsubgr_neg]) ).
cnf(c_168,negated_conjecture,
( k9_relat_1(sK1,C) = k2_funct_2(A,B,sK1,C)
| ~ m1_relset_1(sK1,A,B)
| ~ v1_funct_2(sK1,A,B) ),
inference(resolve,[status(thm)],[c_64,c_65]) ).
cnf(c_169,negated_conjecture,
( k2_funct_2(A,B,sK1,C) = k9_relat_1(sK1,C)
| ~ m1_relset_1(sK1,A,B)
| ~ v1_funct_2(sK1,A,B) ),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_222,plain,
( r1_tarski(k9_relat_1(A,D),k9_relat_1(A,E))
| ~ r1_tarski(D,E)
| ~ m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))) ),
inference(resolve,[status(thm)],[c_87,c_85]) ).
cnf(c_1991,negated_conjecture,
( m1_group_2(k5_group_4(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_125]) ).
cnf(c_1992,negated_conjecture,
( m1_group_2(k5_group_4(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_133,c_1991]) ).
cnf(c_233,negated_conjecture,
( m1_group_2(k5_group_4(sK0,A),sK0)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_132,c_1992]) ).
cnf(c_1993,negated_conjecture,
( v1_group_1(k5_group_4(sK0,A))
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_124]) ).
cnf(c_1994,negated_conjecture,
( v1_group_1(k5_group_4(sK0,A))
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_133,c_1993]) ).
cnf(c_234,negated_conjecture,
( v1_group_1(k5_group_4(sK0,A))
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_132,c_1994]) ).
cnf(c_1995,negated_conjecture,
( r1_tarski(A,u1_struct_0(B))
| k5_group_4(sK0,A) != B
| ~ m1_group_2(B,sK0)
| ~ v1_group_1(B)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_134,c_118]) ).
cnf(c_1996,negated_conjecture,
( r1_tarski(A,u1_struct_0(B))
| k5_group_4(sK0,A) != B
| ~ m1_group_2(B,sK0)
| ~ v1_group_1(B)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_133,c_1995]) ).
cnf(c_240,negated_conjecture,
( r1_tarski(A,u1_struct_0(B))
| k5_group_4(sK0,A) != B
| ~ m1_group_2(B,sK0)
| ~ v1_group_1(B)
| ~ m1_subset_1(A,k1_zfmisc_1(u1_struct_0(sK0))) ),
inference(resolve,[status(thm)],[c_132,c_1996]) ).
cnf(c_1997,negated_conjecture,
( k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK2),sK1,A) = k9_relat_1(sK1,A)
| ~ m1_relset_1(sK1,u1_struct_0(sK0),u1_struct_0(sK2)) ),
inference(resolve,[status(thm)],[c_169,c_128]) ).
cnf(c_315,negated_conjecture,
k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK2),sK1,A) = k9_relat_1(sK1,A),
inference(resolve,[status(thm)],[c_104,c_1997]) ).
cnf(c_1998,negated_conjecture,
~ r1_tarski(k9_relat_1(sK1,sK3),k2_funct_2(u1_struct_0(sK0),u1_struct_0(sK2),sK1,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(paramod,[status(thm)],[c_315,c_126]) ).
cnf(c_316,negated_conjecture,
~ r1_tarski(k9_relat_1(sK1,sK3),k9_relat_1(sK1,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(paramod,[status(thm)],[c_315,c_1998]) ).
cnf(c_372,plain,
( r1_tarski(k9_relat_1(sK1,A),k9_relat_1(sK1,B))
| ~ r1_tarski(A,B) ),
inference(resolve,[status(thm)],[c_222,c_103]) ).
cnf(c_407,plain,
m1_group_2(k5_group_4(sK0,sK3),sK0),
inference(resolve,[status(thm)],[c_233,c_127]) ).
cnf(c_410,plain,
v1_group_1(k5_group_4(sK0,sK3)),
inference(resolve,[status(thm)],[c_234,c_127]) ).
cnf(c_434,plain,
( r1_tarski(sK3,u1_struct_0(A))
| k5_group_4(sK0,sK3) != A
| ~ m1_group_2(A,sK0)
| ~ v1_group_1(A) ),
inference(resolve,[status(thm)],[c_240,c_127]) ).
cnf(c_1999,plain,
( r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3)))
| k5_group_4(sK0,sK3) != k5_group_4(sK0,sK3)
| ~ m1_group_2(k5_group_4(sK0,sK3),sK0) ),
inference(resolve,[status(thm)],[c_434,c_410]) ).
cnf(c_2000,plain,
( r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3)))
| ~ m1_group_2(k5_group_4(sK0,sK3),sK0) ),
inference(copy,[status(thm)],[c_1999]) ).
cnf(c_1983,plain,
r1_tarski(sK3,u1_struct_0(k5_group_4(sK0,sK3))),
inference(resolve,[status(thm)],[c_407,c_2000]) ).
cnf(c_2001,plain,
r1_tarski(k9_relat_1(sK1,sK3),k9_relat_1(sK1,u1_struct_0(k5_group_4(sK0,sK3)))),
inference(resolve,[status(thm)],[c_1983,c_372]) ).
cnf(c_1990,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_316,c_2001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:19:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3623893 was started by sandbox on n002,
% 0.10/0.36 % Fri Sep 25 15:19:35 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.80/0.53
% 0.80/0.53 % given #500 (T,wt=23): 1565 -m1_group_2(A,f2(k5_group_4(c6,k1_xboole_0))) | v3_group_1(A). [resolve(1550,a,164,c),unit_del(a,1552),unit_del(b,1551)].
% 0.80/0.53
% 0.80/0.53 % SZS status Theorem for theBenchmark
% 0.80/0.53
% 0.80/0.53 % Proof 1 at 0.12 (+ 0.03) seconds.
% 0.80/0.53 % Length of proof is 44.
% 0.80/0.53 % Level of proof is 6.
% 0.80/0.53 % Maximum clause weight is 40.000.
% 0.80/0.53 % Given clauses 523.
% 0.80/0.53
% 0.80/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
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